Not a stupid question at all.

You may, in fact, mix and match brands of transmitters and receivers. But there are some limitations.

Talking about only FM here for a moment, as that's most common. With FM, there are two ways to "shift" the signal. Futaba and Hitec go one way, JR and Airtronics go the other. So you can't use a JR reciever with a Futaba TX

Then you get to companies like GWS, FMA, Hitech (with their after-market RXs) and several others. They all sell FM receivers in "Futaba" and "JR" flavors. So, when you order a GWS receiver, you specifiy if you want Futaba compatibility or JR/Airtronics compatibility.

Now, each receiver uses a crystal. You use the crystal that matches the receiver, regardless of the transmitter. So use a GWS crystal in a GWS receiver when using it with your Futaba transmitter.

PCM is a different animal. In general, PCM receivers only work PCM transmitters from the same company, and sometimes not all PCM TXs from the same company. (1024 vs older 512 PCM for example).

And to really confuse things, there are receivers out there that can be switched from Futaba to JR compatible. Hitech and FMA both make some that do this, either with a switch or they actually auto-detect what kind of TX is sending out the signal.

And finally, there are a couple of Transmitters (Hitech Eclipse with the Spectra module and the Polk Tracker II) that can be set to Futaba or JR shift, allowing them to work with any FM Receiver.

Personally, I have a JR and a Polk transmitter. I have a mixture of FMA, Hitech, JR, Futaba (just 1), and GWS (just 1) recievers.