I find analog switch usually label the two terminal of the switch channel as "S"(Source) and "D"(Drain). Such as this. I think they are equal in function, either can be used as input or output. So why still use the terminology from MOSFETs?
Different datasheets might have different conventions. Let's consider the famous 4066, which are bilateral switches (Transmission gates).
Here they call each terminal In/Out:
Here they call In OR out:
Here x and y: