There was once a VISA Europe branch that was separate from VISA .inc, it’s not the case anymore since 2015 when VISA bought back ViSA Europe.

There are countries where debit cards are also compatible with a local system and in those countries, banks make the POS devices use that local system by default (for cost cuttings) if the card is compatible and only use Visa/MasterCard if the card is not compatible.