Yes these absolutely do exist and in many cases are a VERY good way to help your credit score! The way these cards work is you decide on the balance of the card and give that to the bank/credit union. They then put this money on hold in a savings account in your name and give you a credit card to use. Some places require you to put a little extra for credit cards in case you go over the limit.
You still pay interest on these credit cards and must make your own payments, but this way makes it much less risky to the credit union/bank. These are very simple to get approved for, and especially with kids just turning 18 and are just starting to earn their credit.
Also, these cards do affect your credit card the same as any other credit card. I always suggest paying regularly on this card from 12-18 months and then going back to the credit union/bank to ask to take the hold money off hold.