You can use one database, especially if you are wanting to share test elements across different sites.
However, by doing so, you can run into some confusion in the reporting due to different pages with the same name on the different sites. This may not be of concern to you depending on whether you are wanting to track performance at a page level, or at a test level.
You can use different databases or the same one simply by keeping or changing the connection string in the web.config settings.
Another variation of this would be to specific different 'objectQualifiers' in the web.config files, which would then generate two completely separate sets of objects in the database, effectively giving you two installations, but using the same database.