In English, "party" and "fiesta" mean the same thing; a celebration of some sort. Party is an English word, and fiesta is a Spanish word. In the United States, there are a lot of Spanish words that are used in every day English conversation. For the most part, "fiesta" is used only in informal conversations and specific to an event or celebration that is informal.

A fiesta, in English, is more like an organised party for everyone, and not an invite-only personal party. For example, we'll never say "birthday fiesta" unless we mean a really big street party! :)

It is exactly the same, the only difference is that party is in english and fiesta is in spanish