In my experience (~31yrs US, ~2yrs Germany):
USA: debit cards and credit cards are both offered through banks. They operate on the same payment infrastructure (Visa, Mastercard, etc). They are all equally accepted. The only difference between them from a consumer standpoint is that a debit card immediately withdraws the money from your account and typically requires a PIN for purchases, whereas a credit card operates on credit -- ie you acquire debt when you make purchases but your bank account balance stays the same -- and usually requires just a signature, and not even always that. On a credit card, you have a (very high) interest rate, but only on balances that are carried over past the end of the month: if you pay off the entire statement balance by the due date, there's no interest. More concretely: an August statement contains all transactions for August, but you receive it during mid-September, with a due date by the end of September. So by the time you've paid your August credit, you've made more purchases, and the total balance is higher than the statement balance. You only get charged interest on the August debt that is left over after the due date; September debt continues on in limbo until its statement due date. Payment processors make money per transaction, banks make money by the ridiculously high (~20%) interest rates they charge when people don't actually pay off the statement. Both credit cards and debit cards are ubiquitous; you get a debit card any time you open a checking account, and almost everyone has a credit card (77%, and the average person has 3+ cards [1]). You do not need a savings/checking account to have a credit card account at a bank. Credit card debt is extremely widespread, currently over $1 trillion USD for the country as a whole. If a merchant says "No credit cards allowed", they may still accept debit cards, even though they operate on the same payment infrastructure.
Germany: the terms "debit card" (typically "Girokarte" or "EC Karte"; I've literally never heard someone outside of a finance context say "Debitkarte") and "credit card" ("Kreditkarte") are used almost exclusively to describe the payment infrastructure, and only the payment infrastructure. Girokarten operate on a completely different payment infrastructure and are accepted at most in-person merchants and government buildings. Meanwhile "Kreditkarte" is, at least in everyday language, only used to describe the payment infrastructure, and are not always accepted at in-person merchants, and only rarely at government buildings. If a government agency (or shop) says "No payment with Kredikarte is possible", they mean no payment with Visa/Mastercard/etc is possible. Whether it operates as an instant-debit or a revolving-credit basis is completely irrelevant. A Kreditkarte is always through Visa, Mastercard, etc, but a Girokarte never is. That's the primary difference here. Meanwhile, Kreditkarten that actually extend you credit are vanishingly rare in Germany; as a US citizen [2], I haven't even tried to find one, so I can't speak to the internal mechanics of actually having one. But I can say that the vast majority of people I've talked to here simply don't understand what the difference is in the US (I think this is compounded by the language barrier, because like many English -> German loanwords, "Kreditkarte" doesn't mean the same thing as its English root).
[1] https://www.bankrate.com/finance/credit-cards/credit-card-ow...
[2] The US places large reporting requirements on foreign banks offering services to US citizens, making it very difficult to open accounts. Many foreign banks simply refuse to do business with US citizens. As with taxes, there are no exceptions for non-residents ("expats"). In some destination countries it can pose a significant burden to new immigrants.