Pan seems to be gender blind, i.e. attracted to people with no regard to gender or attracted to all genders.
Bi has one definition in being attracted to both men and women, both sides of a binary.
Bi also has a less common usage to mean attracted to more than one gender which may or may not include both halves of the binary or the entire spectrum.
S'okay. I'm pretty new to it myself. I'm reading articles and stuff as I write this.
Using this as a reference: Pan is gender blind, omni is all genders but gender does matter and may include preference, poly is more than 2 but not all genders. Bi is a big tent that includes all of these.
Bi can also mean attracted to the whole spectrum. Really, what it's come to mean is attracted to more than one sex/gender.
I agree with Fleur more that Bi means that you're attracted to multiple sexes/genders similar to pan, but pan is effectively genderblind whereas sex/gender is still a factor for bi folks, it's just not a factor that excludes most people.
But these definitions aren't entirely agreed on. If you feel more comfortable identifying as bi, that's fine. If you feel more comfortable identifying as pan, that's also fine. We're very, very similar to the point that it's common for people to not know the difference. The distinction appears to be more personal.