Perhaps I'm wrong, but I'd expect a FSK receiver to only operate with a FSK transmitter, and a ASK receiver to only operate with a ASK transmitter.
No, that's what I meant, too. Knowing the modulation meant for me to have the ability to demodulate the signal modulated with this type of modulation.
It seems to me that you are looking for receiver that can receiver transmissions from either type of transmitter. No idea whether such a critter exists.
Concerning this, I thought too. And I finally decided to use two devices for this issue. That means one receiver only works with FSK, the other one with ASK. So, I think you're right. It's difficult to find one. The only one, I found, is the ATA5811 - however it seems to be very sophisticated. That doesn't mean I have decided not to want to work with it.
So I will look for one ASK receiver and a FSK receiver separately. Can you recommend one that supports (only)one of these modulations?
They should be as simple as possible, the received data should be given directly at a pin output without trying to decode it.