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site (tables: articles, authors....)
forum (tables: messages, users, logs)
Best to keep them seperate as caching will be more efficient this way I believe. Also would be better for secuirty as you could set different permissions for each database incase a forum member managed to get hold of single password etc.
OK, in both cases table caching, or table permissions could do the same thing but it's easier to administer at the database level.
Another reason for having two seperate databases is that it would be easier to maintain backup scropts. You may want to backup the forum db every hour, and the site db every 24hrs. Again, this could be done with a single database but it's easier with two.