Earlier quoted context omitted.
They don't have the same legal protections for their use. There's hardly ever any reason to use a debit card over a credit card.
In the EU, there are lower charges for the merchant when a debit card is used. Sometimes, this results in a small charge for using a credit card. (Note that TreeCard is an English company, where they have inherited this cost difference.)
This is definitely the case in the US. The fees vary between different acquiring banks, merchant gateways and cards, but generally they follow a pattern similar to the following:
CC - $0.25 + 1-4% of the transaction amount
Debit - $0.25 - 0.50 and no percentage