Poacher's Knife DOES contribute to counter jungling. It gives extra gold, further increasing the gap you're putting between yourself and the enemy jungler, and it gives an escape option so that you can't be caught out at a lower health than you might want to by letting you quickly dash away. Or if you're staying healthy, quickly dash to the next camp if you're feeling saucy to take that one as well before running out. The extra gold and the movement speed buff incentivize counterjungling more while giving you the means to use guerilla style hit and run tactics about it.
If your team falls behind, chances are the enemy jungler isn't spending much time in his jungle because he's applying pressure to the lanes. The Poacher's Knife lets you punish his absence by making sure your allies are playing safe where possible, and using those moments to dive into his jungle while he isn't there to help yourself catch back up. Plus when he goes back into his own jungle to pick up buffs, he'll find that they're gone and that, once again, he's been wasting his time.
None of the other smites help when your team is meeting resistance or falling behind. Stalker's Blade is only useful for chasing, or if someone went and dived your team and you don't want them to get away. But anyone who builds Stalker's Blade likely already has a kit that gives them a lot of mobility options and so the slow is just a small added bit of CC. Blasting Smite doesn't even affect enemy champions, and Challenging Smite is only really useful on AA focused junglers, and isn't doing anything to help you come back from meeting resistance. It helps a jungler snowball, not so much catch up, by adding to kill potential. Trailblazer's smite can be useful for pushing a wave I suppose, but it isn't going to do much to help a champion who's meeting enemy resistance in any way.
For example, a jungle Shyvana only really has two options: Poacher's or Skirmisher's. She benefits pretty solidly from the extra damage and the reduced taken damage of a Challenging Smite, but in all honesty she's going to be dealing more than enough damage of her own not to need the extra true damage burn. She doesn't need Chilling Smite because her W's MS increase is more than enough, and she's got her dragon form's leap if she needs to get on someone right away. Blasting Smite is half useless on her, she has no mana and doesn't need half of it's sustain. However, she's got an MS boosting ability that synergizes well with the boost on Poacher's Knife, and she has a potent dueling kit so when diving into the enemy's jungle, even if she gets caught by them she still has a pretty high chance of walking away with the kill either way. So in all honesty, the ability to roam around the enemy's jungle with that increased movement speed is simply wonderful on her, and lets her transition her role as a lane bully into the jungle by making her already potent counterjungling abilities more so. The entire point of a Poacher's Knife is to make it so that you aren't meeting up with any resistance by significantly weakening the enemy jungler, which is why I explained what counterjungling is and why it makes Poacher's a good item.
None of the smites do anything to help someone who's meeting resistance. Only two of them even affect champions at all, one of them is a slow that might save your life if you're getting pushed, but if you're using it to catch up to a fleeing enemy then you aren't meeting resistance at all. The other one that works on enemies is only good for duelists, which makes it pretty meh in terms of teamfights where you have several people attacking you all at once and it's only reducing the damage from one of them. It's much better on someone who's trying to catch people out like a Nocturne or a Skarner, and again is more of a snowballing choice than anything else. It isn't going to turn a match when there's a five man push on one of your lanes.
You're getting the point of the smites mixed up with what you're trying to accomplish. Try and remember that smite isn't a tool that was originally for fighting other champions. It was meant only to be used in the jungle, and for securing objectives, and it still needs to be treated that way up to a point. Chilling and Challenging smite both give some combat options, but champions who use them probably have enough combat options in their kits as it is, so those are more of situational tools already. None of the smites are there to assist someone who's falling behind unless you use it to get that clutch steal on Dragon or Baron. It's meant to help a jungler keep up, not catch up, but serves the latter in a pinch.
and 
are usefull in any champion fight throughout the game.
can be used oin any jungle camp and even for waveclear in lane.
There is no point in the game where those three are useless.
only work when you can access the enemy jungle, and it doesn't help you do the job like the other items, it only rewards you for being able to do so in the first place.
