Membership
You pay through your Steam account. That way you see the gift afterwards under “My membership” and can end it. We only get your SteamID, nothing else.
You are charged every month. You both see the gift under “My membership”, and either of you can end it at any time. It then runs until the end of the paid month.
Payment only ever happens on feldlazarett.net, never through a link sent in a private message.