Almost all Tristana players I've seen rush IE. Almost all Vayne players I've seen rush BotRK.
Both are champions that are almost exclusively Auto Attack based.
Is there any reason for for this difference?
redniwediS12 votesVayne scales well with attack speed, due to her true damage. Instead of building for large crits you build for rapid application of true damage.
Morsigil5 votesI'm struggling to think of a good metaphor for this situation, but imagine you're playing a resource game where you can buy things with gems, gold, or iron, but you can only buy advantages with one or two of those, not all three. If you spread yourself across all three, you'll have lots of resources but you won't be able to buy the expensive things in any one category.
That's kind of like how damage is in League. True, physical, magical, attack speed, flat damage, crit damage. Spreading yourself across all of them, you encounter the resistances of all of them (except true, of course), and the benefits and downfalls of each.
Vayne is not a crit monster, not really. Her goal is not to crit (she will after 2 PD and an IE), it's to proc her silver bolts. Late in the game she crits, but she's not going to be critting for the kind of damage that Trist does because they build differently. Vayne is about true damage from silver bolts (percent health) and percent health from Bork, both of which cannot be increased with AD but CAN be increased with attack speed. So you focus on doing percent damage with her.
Trist has no innate percent damage, and she has attack speed in her kit, so she wants to focus more on filling in the "missing" damage (compared to vayne, who gets damage for free instead of AS). The way she does that is by acquiring lots of AD and crit, some armor pen, and a little AS. So in other words, Vayne has damage, she just needs a little more, and lots of AS. Trist has AS, needs a little more, and lots of AD.
Getting a Bork on Trist isn't bad per se. If you get it early enough (like first item after you get early kills) you can leverage the relatively large damage boost (80 flat damage per 1000 hp) into a lead. It will eventually fall off though (even, IMO, against tanky opponents). So like you want a bork before they finish their BF sword. Otherwise, that extra damage from the bork does nothing for Trist's crit damage, which is really what she is there to do. Late game, high speed crits.
MrBuffington1 votesDo you know why pro Trist players build BT as their lifesteal item instead of Botrk? I play a fair bit of Tristana, and I usually built Botrk third (unless I needed LW first), but seeing players like Imp and Uzi build BT instead makes me think that my build is suboptimal.
Morsigil2 votesOf course! It's because the attack damage that BT contributes towards the later mid game and late game crits, and the way those crits benefit the life steal. By item 3 (not including boots), everyone in the game has hit some kind of spike and team fights have begun. Picks still happen, less often because everyone has a core or two, but you'll rarely face anyone one-on-one if everyone is on their game. What does BorK do? It changes the balance of duels and arguably chunks high HP tanks.
BT has twice the life steal, and contributes over 3 times the AD towards crits and sustained life steal. That's the kind of item you want on a champ that scales on crit chance and flat ad! That alone would be enough, but on top of that there is the shield you will undoubtedly want when your team engages and you will undoubtedly have because you've been farming (at the very least on the way to the battle). I wouldn't get BT third though necessarily, I would get IE, PD, and then get either LW or vampiric scepter depending on what I needed and go from there.
Vayne = increase attack speed, increase chunks of HP you take from champs. Trist = Increase damage and crit (stats which are on most ad items), increase chunks of HP you take from champs. There is plenty of room for variation though. A Vayne going IE PD LW isn't necessarily going to suck. A trist going BorK won't either. They're all decent picks, it's just a matter of what is optimal, what rounds out the kit, and who you're up against.
MrBuffington1 votesAwesome, thanks! How about Corki building Botrk? That's another one I'm not quite sure I understand...
Morsigil2 votesUnfortunately, Corki isn't a champ I'm very familiar with. I main Trist, Cait, and Varus, and Corki is kind of an odd duck (though not so different from Varus). I'll take a shot at it though.
Bork is apparently a common item on him Corki. Looking at his kit, Corki is caught between Vayne and Trist in that he has incentives to build AD as well as AS. He has percent true damage from his passive which scales off flat AD as well as attack speed, but his passive alone isn't something to be built around as it's only a percentage of his AD rather than their HP. Corki has a little twist in that he is a caster ADC and as such benefits from the mana and sheen boost Trinity Force provides. He also has some armor reduction built into his kit.
Taken all together, we can see that most of Corki's damage comes from his abilities rather than his auto attacks, and he is also a great duelist. During those fights though, while he will be auto attacking, much of his damage will be from his phos bomb, his gatling gun, and his rockets, and as such you want to build to enhance that damage and his duelist ability while fulfilling the role of ADC.
So what do you see people do? You see the trinity force to provide utility, damage that procs on spell casts, and mana for his spells; You see IE as a standard ADC item for damage; Last Whisper which builds on the armor reduction already built into Corki's kit; blade of the ruined king to add percent damage on top of his true damage and to add flat AD damage to his auto attacks. Effectively BorK provides duelist utility and helps diversify Corki's damage. Most champs can't really get away with that, but as I said Corki is an odd duck.. you want that AD to round out his true and magic damage (so no one can defend against you well) but also to make use of that free armor reduction in his kit. The flat chunk of AD damage you get from Bork autos will go much further as a result of gatling gun and LW, making your autos hit for significant AD despite only having one big AD item.
tl;dr: Corki has a lot of damage in his kit, and it's hard to itemize to support both his ADC role and his caster role. His standard build (inclulding bork) does that by providing utility, armor reduction, and flat AD that make his autos hurt, while retaining the strength of his abilities and making him a superior duelist.
MrBuffington1 votesThat's really helpful, thank you! I usually get stuck in the trap thinking that champs with AD ratios want to build AD, while champs that are AA reliant want to build Botrk (which is why I was confused about Trist, who's mostly AA based, builds BT, and Corki, who's more of a caster, builds Botrk). Your explanations help a lot, thanks!
Caustic Crusader3 votesTristana doesn't need the copious AS boost due to her Q and Stakikk Shiv/Phantom Dancer being more than enough. The active is also too short-ranged and irrelevant since her W and R are also massively powerful disengage tools with superior effectiveness.
Vayne, on the other hand, has nothing beyond 550 range, and her Q and E aren't as powerful disengage. On top of that, she needs a ton of AS, and also her W synergizes very well with the %health damage of BotRK.
Deep Terror Nami2 votesProbably because Trist has her own AS boost and can focus on AD. Sometimes ppl get Shiv on her too which would make BotRK even less needed. At least that's my theory.
s7efen2 votesTrist outranges the active.
TehNACHO2 votesVayne is the supreme anti-tank ADC, and coincidentally, Blade of the Ruined King is an anti tank item who's anti tank abilities scale on the same stats as Vayne's (in this case, Attack Speed).
Spreek2 votesThere's a lot of reasons but there are two big ones:
Baughwssery2 votesIt's funny that everyone talks about the true damage, but in most of her games Vayne's overall damage is only about 20-22% true damage. People build for it, but it only accounts for about 1/5 of your total damage output.
Morsigil1 votes"only... 1/5th of your total damage". So lets start at 1/5th. Add bork. That's...2/5thish? Bonus from ult, and her stun. Probably 3 to 4/5thish? So most of her damage is from her kit and bork. You say, "people build for it". No. People don't build for her true damage. They build to synergize with it. To make other things happen while it is happening, and to make those things happen more often.
RadicalGG1 votesTrist owns attack speed boost, so building AD and crit will help her early, + his pushing ability due explosive shot. In the other hand silver bolts true damage + the high ad scaling Vayne has makes BOTRK a perfect buy, adding life steal, attack speed and active for dueling to its arsenal.
Death in 4 Acts1 votesVayne scales off AS Hence why you see. 
But Tristana has a huge AS buff on top of safe damage. So you build her for crit damage early and then the comes in when they have alot ofhp and you need to tank melt. If they have no HP you can go ahead with 
ReaverCamera1 votesNot to mention she benefits immensely from the active to chase down opponents. Trist just jumps at em.
Nick Valentine1 votesI find Trist doesn't use the active as much as other closer range can and doesn't require the very important slow. Her goal is to W away and then ult away while maintaining dps. She certainly can use the active but why does she need it?
Katsa1 votesVayne has true damage, she scales well with attack speed and lifesteal. Tristana doesn't have true damage, so crit and AD really helps her increase her damage. Her Q already gives her a ton of attack speed too. Also, she has a lot of range, late game, it wouldn't make sense for Tristana to move closer just to use BOTRK.
