It is normal that user login would be all messed up. To correct the action there are a couple way to fix your problem.
1. EXEC sp_change_users_login 'Update_One', 'Mary', 'NewMary'
2. delete all user from the new server and script the user from the old server and execute it on the new server.
That should be ok don't you think?
OK here is what you told me. When you create a login, the application create another one for it's use so that mean for each person there are 2 user id is this correct?
if you do select name from sysuser you would be able to correct all of them. Also make sure all the logins are created on the server first before you try to correct it. There are ways to copy logins from server a to server B (if it is sql 2000 ) and it will preserve the password if it is a Sql account too.