What is the difference between team site and community site? When would you use one over the other?
In general, team sites are more focused on content. They are meant to be used as "a single environment to create, organize, and share content." Features of this site type include: shared docs, announcements, calendars, links, tasks, discussion boards. These sites are good for document management or when the site is focused more on providing content and information.
Community sites are meant as an interactive and (somewhat) social area. This type of site is best for facilitating interaction, messaging and collaboration.
I don't really use this type of sites, but as I understand it, they are useful for message boards and communication.
hoffie4 is correct, but let me say that each of these is merely a template or jump start of a site. They are actually the same thing. You could start with a blank site and get to either one by creating libraries/lists or activating features. Just find the one that is closest to what you want and add or subtract elements to get what you want. I usually start with a team site and modify the navigation and start page. Most users don't use the calendar or discussion board, but I leave them there.
So to answer your question, create one of each. Determine which one is closest to what you want and delete the other. Try to remember that as soon as you modify a site, it is no longer the same as the template. Good SharePoint sites are not static. 5 minutes after you create it you will no longer have a team or a community site, you will have your site.