Long protocol tends to be the default for women with normal ovarian reserve
Short protocol tends to be the protocol of choice for both (counterintuitively) poor responders (low AMH) and high responders (high AMH / PCOS)
There are actually two types of short protocol - 99% of the time when anyone mentions short protocol, they'll be referring to a short antagonist protocol. There's another kind of short protocol known as a short flare protocol (a short agonist protocol) which is rarely used for poor responders
For all intents and purposes I'd ignore the latter and assume that short protocol means a Cetrotide or Orgalutran protocol
I am currrently on long protocol (despite pretty low amh) never really got an explanation for this! Suspect due to being 34 and conceiving naturally previously.. My spray started on day 21 and the notes said to use non hormonal protection from your period of the cycle before starting the spray, i.e. Day 1 of the cycle where the spray will start on day 21, and do so until the end of the 2ww, due to all the hormones involved.. didn't apply to me as I cant conceive naturally but must not be a good idea to take all the hormones if you even have the slightest chance of conceiving yourself.. good luck!!