Earlier quoted context omitted.
It's not. It is an electronic money institution, which is far from a bank, it can only keep customer funds and process payments.
I don’t know the difference, but it does say that on the tin: https://www.paypal.com/lu/webapps/mpp/about > PayPal (Europe) S.à r.l. et Cie, S.C.A. is a credit institution (or bank) authorised and supervised by Luxembourg’s financial regulator, the Commission de Surveillance du Secteur Financier (or CSSF). CSSF’s registered office: 283, route d’Arlon, L-1150 Luxembourg.
Can't comment re PayPal specifically.