Simon, the debit card is issued by your bank and acts as a debit from the ATM or a charge card. The PIN is needed at the ATM but when making a purchase if you have the clerk run it as a credit versus debit charge then no PIN is needed. Also you save the establishment a surcharge fee they pay on all debit purchases. The visa check card is issued by visa and acts the same way. I see no benefit for the check card as you need a bank account anyway.
I also am surprised at the "numerous" card problems. I guess I am very lucky as I have never had a problem with either my credit card or my debit card account. In the years of working in retail I can also honestly say that most card account "overcharges" we had called in were due to employee theft and fraudulant use of a cardholders number, this rarely happened. Our system also never printed the full account number on the receipts but the registers had electronic journals that held the full number and could be looked at to get the rest of the numbers. Of course the handfull of times the theft issue did ocur the employees were found out, they were arrested and of course terminated. I would not encourage anyone to allow their card to be taken out of eyesight of them or have an imprint done if you do not personally "know" the business/person. I once followed a clerk at a dive shop in Key West into the backroom, as he walked off with my card speaking a language I could not translate. I thought that the card machine may have been back there and I did not want it out of my sight and it turned out there was no machine back there and he quickly made a U turn back to the shop area and ran my card. It does not hurt to have a Healthy mistrust sometimes.

"All people smile in the same language"