[Wilfred1]

I would be looking at sharing the vBulletin user table with CS-Cart which is an ecom application.

But as an example between vBulletin db1 and db2 you would:
1. rename the user table in db2 to user_old
2. create a view of the user table from db1 in db2 by running script in db2:
CREATE VIEW user as SELECT * FROM db1.user;

In the case of CS-Cart you would need to do some other work with the queries to match but your question was "How would you share a table across two databases ?"