In terms of probability it is clearly different but in terms of opportunity it is certainly the same, even though the conditions for a big club clearly have more advantages over the favorite but they still can't make it seem like the small club isn't there.
Now for the Champions League there could be some unexpected forces. Newcastle with the power of money and their passion to be better or even another club that is not really a favorite there could be several conditions like that during the 2021/22 season for Villarreal and last season for 3 Serie A clubs which were even surprising in the quarter final .
Even though the championship is still about how pots and clubs subscribe in terms of probability but still in terms of surprises for the Champions League, clubs like this with ordinary strength often do it.
If we see it like a team have the chance to become the Champions League champions as long as they haven't been eliminated yet then yes. In this situation we can see it like even the weakest team of the tournament have an opportunity. However I don't think the majority of people would think in this way while assessing the teams that can win the title.
People always look at how strong these teams are. Then they classify what teams can really win this title considering the strength and success factors. Of course not all the time the biggest title contenders win the title. For example Chelsea won the Champions League title in the 2020/2021 season while not many people were giving them a chance. Of course Chelsea are also a top team but they were trailing behind many others you know.
But when we look at the general history of the tournament the champions are nearly always the most performing teams with quality players.
Clubs that are considered to be favorites cannot be said that they will become champions, and small clubs that are considered only dark horse clubs have the opportunity to surprise, as in a football match.
The things that might factor into how we classify them as you said obviously are a consideration of what results we analyze about what will happen in the competition.
All clubs have a chance, it's just how many percent we will give them chances, like for example We will definitely give Manchester City big chances the same as we will give chances to weaker clubs, but the difference is how many points we will give to rate them.