So since I am someone who considers himself pansexual I can give a bit of my own thoughts in the bi vs pan thing. Obviously can't speak for all pan folk, but having talked to a bunch I feel pretty confident in what I'm going to say.
While the term does have a history in, essentially, a misunderstanding of bisexuality as denying trans and non-binary people, the current definition is very similar to bisexual, but with a specific difference:
Bisexual is being attracted to two or more genders. It doesn't need to be ALL genders, it just needs to be at least two.
Pansexual is being attracted to people regardless of gender. By that I mean the gender of the person doesn't matter at all, you'd be attracted to them with whatever body.
For me, the reason why I prefer pan over bi is because I really don't care what gender someone is, I can work with it all. What matters to me is that I like the person and we have some good chemistry. I don't even really worry (and sometimes don't even know) about what genitals I'll be working with until the pants come off and it's time to do my thing. While yes, some of the things that attracts me to a person are secondary sexual characteristics (I love me some good tits and hairy chests) the distinction is that I'm attracted to all varieties of it. So for me it doesn't matter if a woman has a pussy or a cock, I can still be turned on and want to pleasure that pussy or that cock. Because for me it's more about making the person feel good than it is doing any specific act with any specific body part.
That being said, I do always joke that I consider myself pan, but I'll say bi if I don't feel like explaining it, and I'll say I'm gay if I REALLY don't feel like explaining it.
Hopefully that wasn't too confusing.