I was asked about the difference today. The only difference I know is that mayday doesn't appear in the exams ( like the SOS parts of the book, you get the joke? :) ). I also found the difference in the origin, but:
What is used in aviation? Both are equivalent or there is actually a difference and the one should be preferred over the other?
SOS is a distress signal. In the context of aviation emergency calls it would be equivalent to a Mayday call, which is the standard voice signal for distress.
There is, as far as I'm aware, no standard equivalent for an "urgency" (pan-pan) situation in morse code.
As far as its use in aviation, most aviation communication today is by voice (radiotelephone), and "SOS" is not generally used in voice communication.
Its used by morse code stations is because it is a short and easily recognized pattern:
. . . - - - . . .
Its recognizability is part of the reason it replaced the old Marconi CQD general distress call code
- . - . - - . - . - . .
which was literally a general call to all stations (CQ) signaling "distress" (D).
I can't find a reference, but I would assume there's at least one case in history where the SOS code was used by an aircraft (back when morse stations were common on aircraft).
An SOS signal could of course be transmitted today using the unmodulated carrier from your radio by simply keying the microphone, but that would only be useful if the voice circuit of your radio has failed and you had no other means to communicate. Otherwise voice contact or setting your transponder to an appropriate code would generally be the preferred way to signal distress.
The "SOS" prosign is for use with telegraph (typically Morse code) transmissions.
"Mayday" is for voice (radiotelephony) transmissions.
Therefore, as long as your radio(telephony transmitter) is working, you should use "mayday" if in your judgement doing so is required. "SOS" should not be used on radiotelephony. Saying "ess ooh ess" or, Heavens forbid, Sierra Oscar Sierra, might get you some attention in spite of that, but I can see no reason whatsoever to go out of your way to use nonstandard phraseology when a perfectly good (and internationally recognized, and drilled into one's head from early training) standard alternative already exists.
If for some reason your radio isn't working, then squawking 7600 or possibly 7700 and simply executing the proper loss-of-communications procedures for the airspace you're in is likely to be better (and will certainly be more readily recognizable) than trying to signal SOS via an intermittent, unmodulated AM carrier, which will come across as little more than clicking to anyone listening.
Your radiotelephony training and examination should have covered emergency communications, including the use of mayday. Mine certainly did, both on the theoretical as well as the practical examination. Thankfully thus far I haven't had to use that in real life.
Compare the extensive discussion in Why do airplanes use MAYDAY when in danger but ships send SOS?
-.-. --.- -..in modern (ITU) Morse code.-.-. --.-. -..might beCĜDif https://en.wikipedia.org/wiki/Morse_code#Letters,_numbers,_punctuation,_prosigns_for_Morse_code_and_non-English_variants is to be believed. It's probably close enough to be recognizable, but it's not correct. – user Oct 20 '18 at 17:58