As far as I'm aware, pansexual means bring attracted to a person regardless of their gender, which can be literally anything in the whole spectrum of genders. Bisexual on the other hand would mean sexual attraction towards two genders, traditionally male and female, although the definition is slightly more flexible. I've seen it refer to sexual attraction towards two or more genders, which basically suggests that gender plays some role in the attraction, as opposed to pansexuality, in which sexual attraction is independent of gender. Obviously, I'm not really an expert of this you might want to take my word with a healthy amount of seasoning.
I would agree with Brytaleith's second definition, which is that bisexuality is attraction to multiple genders, whereas pansexuality is attraction to people regardless of gender. Not necessarily a huge distinction, but some people may find it important to make that distinction in their own identity
for me the difference is that a bisexual person uses gender as a part of what they consider when assessing a potential partner. Even if all genders are fine for them, they do take the gender and, orientation of the other person into account. I, as a pansexual person, do not think of people as having gender unless they tell me what gender they are and, I don't evaluate potential partners based on gender or orientation at all. If I'm interested, I'll let you know that regardless of your gender and orientation. I don't expect anyone to find me attractive just because I find them attractive, I just don't beat around the bush. Honesty has never ruined a good friendship, if they are that foolishly touchy, they won't hit it off with me, even as friends.
For me bisexual is someone who likes men and women Pansexual is someone who is attached to all genders.
Bi =Two genders Pan = All genders I don't believe there is much difference. Plenty of bi people consider themselves open to everyone.