After install 3.8.5, I show 3.7.4...
 

I just installed 3.8.5 on a new website. Everything shows 3.8.5 at the bottom of the screen and it looks correct.

Next I want to get all the members, threads...ect from the orginal website transfered over. So I copy the sql and loaded it in. By doing this now for some reason I'm getting 3.7.4 version and the original website themes. It looks like I'm copying the entire program over and not just the data.

I don't understand how importing the database changed the version number. What am I doing wrong? Does anyone have the steps to copy just the data to a new host?

Because the database contains information for 3.7.4
You would have to upload the 3.8.5 files, then run the upgrader to update the database.

Indeed. You restored a 3.7.4 db on a 3.8.5 forum. You either ned to run the upgrader so it can bring the db up to date, or upgrade the main forum at th eold host to 3.8.5, export the db and import it at the new host. But the first method would be faster in your case.