Unfortunately, I do not know about the raw MySql files, so I can't answer that question. Hopefully another guru will reply with a solid answer about that.
What I can offer you is to tell you that phpMyAdmin (You do have that right?!) has an export feature that can create entire schema building scripts as well as scripts to insert all the data. So you can go into db1, click the Export tab, choose a single table or multiple tables, click the data option, and export out a file that has insert statements for every row in the table. You can then run that file within phpMyAdmin against db2 to insert all the data. If you didn't already have your schema setup in db2, you can use the export feature to create a schema creation script based on db1, then run that on db2 to create your tables.
If your tables are very large, I'd think a route that copies the raw files would be easier---assuming that is possible. Please post back here to let us know what you end up learning. :)