At very very very nitpicky technical linguistics (and daft) interpretation bi would mean two genders but in common tongue it has the meaning you say. However some would rather not have even the slightest linguistic link to the binary (two).
Edit I could actually be wrong it could also mean sexualities hetro and homo which covers all
Pretty simple:
Bi: Attracted to more than one gender.
Pan: Gender is not a factor in attraction (aka nominally attracted to all people of all genders).
So as an example, you can be bi but have a preference towards men or women, that would be not be congruent with being pan.
At very very very nitpicky technical linguistics (and daft) interpretation bi would mean two genders but in common tongue it has the meaning you say. However some would rather not have even the slightest linguistic link to the binary (two).
Edit I could actually be wrong it could also mean sexualities hetro and homo which covers all