In many cases 1 leads to the other.
A champion being 'annoying to play against / deal with' can indirectly mean it's OP.
I always hated how the old Darius made any other melee top lane pick a lost lane (and a ranged pick a probable won lane). If you want to go a melee top, you're afraid of having to go up against him (especially as someone who played top least of any role). It's not that the champion has a really high win rate (enough people pick ranged in to him to keep him losing) or that a champion isn't balanced overall, it's that the champion is OP in terms of "against what you're playing".
Call it a counter if you like, but I think there's a difference. Sivir is a Caitlyn counter - she can spell shield the Qs, traps, and Rs all day long, She can out-push her. Caitlyn can still deal with Sivir though - she can dodge the Qs and harass with auto attacks from longer range when Sivir's Q is on CD (and just not use her Q, or just poke the support / waveclear, and use W as pseudo-wards on the main gank bushes as opposed to in the lane bushes). Sivir nullifies a lot of Caitlyn's strengths, but if the Caitlyn player is better she'll probably still win against the Sivir.
In contrast, take something like Mordekaiser bottom lane against pretty much any marksman. That lane is going to be unfun. Unless there's a gigantic skill discrepancy or lots of jungle pressure, Mordekaiser is going to win lane by default. The enemy bot lane is just going to farm and try not to feed. Not only is that "annoying to deal with" but in a sense it's OP. Even if you'll outscale Mordekaiser, you didn't pick Corki for example to outscale the enemy ADC, you picked him to play a whole game with. So even if Morde gets to a 49.8% win rate he'll still be OP because he's not fun to lane against. He ruins your game. You want to DO something, you want to feel like you're having an impact on the game. You're not picking Nasus/Kog'maw with the intention of farming up to late game then winning 1v5, yet you are being forced to play that way by an enemy's pick. Your opponent shouldn't get to dictate YOUR playstyle (to the extent that you have to play a certain way if you want to win).
I enjoy laning phase, often more than the other aspects of the game. Yes, I've played Nasus and enjoy that too. When I pick Nasus though, I pick him with the intention of farming as much as possible and becoming unstoppable - so playing that way doesn't bother me. When I pick Jinx and the enemy picks Mordekaiser, I'm being forced to play as if I'm Nasus, except fully with the knowledge that I WON'T be able to take on a fed enemy top/mid/jungle so if any of my teammates lose hard the game is completely out of my hands because there's NOTHING I can do to get a similar amount of gold while laning against Mordekaiser (whereas in contrast, a Nasus without kills CAN deal with a fed enemy mid/jg/adc). I'm picking Jinx with the intention that regardless of who I'm against, if I outplay them I'll be able to build myself a lead and take on whoever on the enemy team is getting fed. Often I actually do that by establishing a 30-50cs lead then securing a kill with the item lead, but that's irrelevant - the point is that there shouldn't be a pick which makes me unable to do ANYTHING to stop the enemy mid laner that's 3-0 after 8 minutes because I'm 0-0 and just have 25 more CS (and am levels behind because duo-lane and they're naturally a better roamer so watch out, I'm going to be their next meal).
has been gutted, he has a 42-43% winrate and a high skill ceiling, but I still find laning against even a half-competent Azir incredibly obnoxious. I know how to beat 
in lane most of the time since I see him so often, but I still just flat out don't want to deal with him most of the time. I feel like a lot of people ban champions due to a combination of not wanting to deal with them and not knowing how to play against them, i.e 
and many more. Some champions are flat out OP and need bans, like release re-work Skarner, but with someone like Yi; everyone knows that you need to shut him down and push advantages before he gets sated and to CC and try to blow him up, but a lot of people don't want to have that pseudo time bomb in their games and again, may not know how to do the above. Or how a champion like Garen or Irelia can lose land hard and still wreck face if your team makes a mistake against them. Or how Mordekaiser is just flat out unfun to fight, let's face it even with the nerfs going up against a Mordekaiser duo lane is still stupidly annoying unless they're braindead. I just personally seem to think that, while some people do ban champions thinking they're OP, a lot of times it's just because they don't want to deal with that champion regardless of the chances they'll see them.
because he is a huge pain in the ass, and 90% of the time no one has a problem with it.