When you restore one database from server A to server B, the user ID in the restored database should already exist on the server B prior to the restoration, otherwise it will cause some security conflict. To solve this problem,
1. Use the sql server built in utility to generate the scripts about the login Id on server A and apply it on server B, then restore the database to server B.
But the passwords won't be transferred to server B , which means you have to add the passwords manually if you want to keep them .
2. If you don't care the difference of the security between two servers, you may use DTS to transfer the data only .
3. use system stored procedure sp_change_users_login to map the login id with the user id in the database.