This is a pretty common question, and personally I use them interchangeably, but bi is not really distinct from pan under most definitions that are internally consistent.

Even linguistically the roots of homo/heterosexuality are same/other. As such if you are bisexual you are both homo (same) and hetero (other). Whilst linguistics is not prescriptive, it still gives us insight into the historical understandings that have birth to an idea.

In the end, be bi, be pan, identify however you choose and never listen to someone telling you that your identity is not what you choose or feel. :)