There's really no difference between a starter check and a counter check.
Some banks use different terms to mean the same thing when it comes to starter checks and some banks call them counter checks and some banks call them starter checks.
A counter check or starter check is just basically an over the counter check from a bank that allows you to write checks to pay bills, rent, or anything else while you're waiting to get your regular checks in the mail.
You should get your regular checks in the mail within 5 to 7 days once your bank orders them.
The checks usually come from a different company who the bank orders the checks from and then the company mails the checks to you.
You can also order checks online and usually get the new checks much cheaper.