Do they still give you a boarding pass, and a seperate piece of paper stating that you have a reservation, but does not in itself act as a reciept nor boarding pass?

Also, that example is bad to begin with, because airlines will oversell their planes ALL THE TIME. Spirit and Fronteer literally try to oversell every single plane on purpose. The idea being that they can try to convince you to get reimbursed with Fronteer bucks. A fictional currency that is only good within their company and has no outside real world value. Then they hope that you take it, and then later that currency expires. Meaning in the end you paid for an airline ticket that you never used and have no recoarse to get refunded.

And a lot of people hate that process and prefer to be able to book a specific seat.