There isn't a standard answer to the problem, the solution varies from script to script. Anyway, what I can say is that having the same MySQL database isn't a solution as-is.
Usually the registration data is kept in one or more tables specific to the script(s) you're using. To avoid to request a double registration you'll need to keep the two (or more) tables in sync in some way, usually through a 3rd script or some modification to the original scripts you want to integrate.
This is all I can say about the general problem, without the knowledge of the scripts you want to integrate.