If an aircraft breaks down, and the airline charter another aircraft to operate the service, it is usually ACMI. Everything else is already in place. The ACMI aircraft steps in and operates the route. I once operated a whole week of ACMI charters for Air Europa, but usually they were one or two days.
Wet lease usually extends for months and includes crews being based away.
Talking of Air Europa, we were in a Swedish registered Tristar at Madrid, but with an Air Europa flight number. We were inching fwd to the departure runway, and were finally handed over to the tower when we were front of the queue. So we sat and waited. Lots of Spanish chat on the radio, but nothing for us, and nothing took off for a couple of minutes, until the tower twigged that we didn't understand Spanish!
Noric East provided the Aircraft, the Crew, the Insurance and Me (Maintenance).
Air Europa arranged everything else, passenger handling, clearances, hotels, transport etc etc.