What is referred to as a series effect loop is really called an insert point, such as on some mixers, placed just after the channel input, to go out to maybe a preamp, compressor, effects or EQ in series and come back into the same stereo in and out jack to continue on thru the channel strip.
A parallel loop really is a loop. I have one amp that will do either or both series or parallel. Most amp companies do not tell if it is series or parallel.
I use signal processing in series, and time based effects in parallel to get the cleanest, clearest sound quality.