All crystals (should) have a number stamped on them indicating their resonant frequency. The TX crystal indicates the frequency transmitted to air, whether it AM or FM. The S/C RX crystal matching has a number offset by 0.455MHz. There is a local oscillator in the RX that this runs, the output is mixed with whatever comes from the aerial, (your TX signal plus everything else in the world) and is passed into an amplifying filter, called an IF stage. This is tuned to 455KHz, and, due to some magic maths, amplifies your signal and almost nothing else.
A dual conversion set repeats this performance, making the "almost nothing else" into "nothing else". There are usually two frequencies involved in this, using a bit of magic electronics it can be done with one crystal, but this needs a different offset to that required for single conversion. Different manufacturers tend to come up with different answers, so while single conversion crystals are fairly universal (honest!), dual are not, and should be regarded as manufacturer specific.
I remember seeing a Futaba list a while back (but can't find it now of course) where both dual and single sets were listed. The TX ones were the same part number for both, but the single and dual were different.
Not all of the TX battery's power goes up the aerial, quite a bit vanishes into the electronics.
