Two FBA sites

I would like to setup a another site with FBA login.

Will the two sites use the same user database?

A FBA user will never have acces to both sites.
I the site is on the same web application, then yes, they will share the same database. If you use a separate web application, you can choose to use seperate databases, a single database, or a single database with multiple "ApplicationName's" (This acts like having separate membership databases live within a single database).

Even if they share the same database, you can still assign different permissions to users on each separate site.