These cards used to be called EC card, however MasterCard now has all the rights to the EC brand. In fact debit MasterCards with EC branding are starting to pop up now.
You either want to speak of "girocard" which is our own payment network or "debit cards", which includes the likes of Maestro V-Pay, but also some Visa and MasterCards. In the same sense, you don't need a credit card for most online shops, you just need a Visa/MC (some will only take credit, but most will take debit).
And as for PayPal: they don't use your "EC card" either. PayPal offers to process the charge by way of direct debit, which is (now) a SEPA process and totally unrelated to any debit or credit card you may have. It just so happens that girocards list your SEPA account info.
/rant. Sorry, this is just one of those things that gets me.