Elliquiy ranks for each of these terms, and people often see them differently, wanting something different in every case. Some just want to know they are playing with adults, others just want to have the possibility for sexual situations open. Still more want to explore sexual themes that are not easy to find in other venues.
Semantics is always a dangerous beast. A pair of words spoken by one person do not necessarily mean the same thing to a listener. Here are some generally broad definitions of the following terms:
Erotic Role Playing almost always refers to roleplaying that involves sexual themes. At the very least, it involves suggestive themes - not all erotica leads to sex after all, though most people who search for it are looking to at least explore the possibility.
Mature Role Playing usually refers to "mature" in the sense of "capable of handling mature themes." This is not necessarily sex, but rather dealing with adults - or people who act like adults, at least - and topics that may otherwise not be appropriate for children. A large number of people come to Elliquiy in order to be sure that the bar is raised in terms of the quality of their writing partners.
Sexual Role Playing has multiple definitions, primarily because of Literotica's SRP forums and the general population referring to the term as dressing up in costume and acting out various sexual fantasies with your partner(s). The former context - roleplaying that involves explicit sex - is typically what is referred to here, though some people come to Elliquiy expecting to find more information on dressing up. Many couples have mentioned that Elliquiy has enriched their sexual lives.
Adult Role Playing is by far the most common term people find Elliquiy with, rivaled only by "Adult RP". It is an 'all of the above', phrase. Most people who use it to find us have found what they want in one form or another.
The short of it is, Elliquiy is a community of adults who role play together. RP here can and often does include sex, but this is not always the case. If you found us using the term, there is likely a niche here for you.
Enjoy your stay : )