It's usually based on the chip settings. Rules aren't as simple as "always online" or "never offline"; an issuer can e.g. convey that they'd prefer online transactions for certain types of payments, while offline is ok for others, via relatively complex configurations of the code of the chip application.

Before that, there was the service code on the magnetic stripe, which also can convey things like "online only" or "domestic use only".

The BIN is only involved in risk management on the terminal's side: Many of these in-flight terminal accept deferred online transactions, which means that, even though they're completely offline, they take the risk of accepting an online-only card. (For truly offline capable cards, the risk is often with the issuing bank.)

That type of risk management can benefit from knowing what type of card it is, and prepaid cards are often seen as riskier (because customers might intentionally drain them before a flight). Of course, debit and credit cards can also be empty/marked as stolen, but these are marginally harder to get and replace.