Earlier quoted context omitted.
Dunno, in a lot of europe, though credit cards are readily available , most of my family (I have relatives in Germany, Austria, Slovenia, Croatia) doesn't have or want them. They have forms of payment which are strange to me but basically are some form of bank debit card, accepted everywhere. Or fancy phone / app payment methods we can only dream of here. I didn't read the OP as necessarily implying technical or cult…
When a form on a web-site says CC (Credit Card) I can always pay with my debit card. (Unless you're talking about another sort of debit card that isn't what I call a debit card - "a MasterCard/Visa/etc with no overdraft). To me it seems like some people use the term "credit card" for any bank card, while some actually mean the "credit" part. While "credit" (non-debit) cards don't seem to be THAT popular in the Europe…
For Germany, a German debit card (the "other sort", as you put it) isn’t the same as any other. It doesn’t have Visa or MasterCard co-branding like other countries’ debit cards, nor a 16 digit number, so it can’t be used online. I might also use the term "bank card" for this, because there are actual debit cards with Visa/MC co-branding which are available in Germany, but less common than other types.
It's also common for Germans to use "Kreditkarte" to mean anything with Visa/MC co-branding, which probably spills over into English. This also leads to the hilarious term "echte Kreditkarten" (real credit cards) for cards that actually have a rolling line of credit attached (these are rarely offered).
However, in the UK I recall that people are usually specific about whether they mean a credit card or a debit card.