Ranting 1million Ezreal mastery here, TL;DR at bottom. Going hybrid instead of AD is situational and does 100% change how you play. Instead of poking, you make picks on squishy targets by yourself. Your Q's aren't as strong, but if a squishy or a bruiser that's behind steps up out of position for any length of time, you can just assassinate them. Your ult is also better at stealing barons or forcing people off of it because of the MR shred from Baron and the huge AP you have. AD Ezreal can.. sort of do all of those things as well, but the time to kill goes from ~.5 seconds to needing an extra auto or two, which can often get you caught out, so you have to actually just poke a bit before you try that, but then your mana is lower, so you're doing less damage on your assassination combo, and it gets iffy.
Hybrid Ezreal is, as a result, far less team reliant for aggressive and risky plays. You make something happen. AD Ezreal is much better at dealing with getting jumped on by a bunch of goons, because he has better options for resists. Hybrid Ezreal is sort of forced into Luden's --> Gunblade, leaving only one defensive slot as his last item. By then, the game should honestly be over, too. AD Ezreal can afford much better defensive options and tank killing options, so he's more about outplaying dives and forcing enemies to overcommit if they want to take him out. This works way better with helpful teammates, though, whereas Hybrid can just force a pick and then your team can see it's 4v5 and start actually doing something. I feel like Hybrid is extremely good in lower elos and against certain higher elo comps where you're not too threatened by their champs in general, and AD is overall just better if they have a lot of people who can stick on you, and your teammates are responsive to that.
The only similarities in how Hybrid and AD are played is that he's staying at the 1000-1150 range of the closest champion, but the difference is what he's going to do when someone steps into that range. Drastically different. It becomes the same if you're hybrid against bruisers, because you have to poke them before trying to outright kill with a combo if they overstep, but at that point you're much better serviced by Bork and a defensive item over luden's and gunblade, and should be playing AD Ezreal, anyway, unless their only ahead person is someone you can oneshot on hybrid but not AD, then it's sort of a tossup. But for the most part, they do play very differently with an overlap here or there depending on the situation.
An example: Hybrid Ezreal vs fed Assassin. He stays out of their range, and their vision if possible, and fishes for a W. Q while W is on cooldown, and if you land the W, you just oneshot them before they can kill you. AD Ezreal vs the same assassin would have bork and a defensive item, poke them a bit, then try to bait them into overcommitting by pretending you walked too far forward once their health is low enough that you can kill them before they kill you. If they don't overcommit, you just keep poking and force a back, or force the kill depending on the situation, but AD Ezreal takes longer to outplay said assassin in an aggressive situation, which gives their team more time to react, rotate, etc. making the aggressive play a lot more risky.
TL;DR, going Hybrid on Ezreal does actually change how he plays compared to AD.