@MUR here’s some initial help:
(1) A “Radio Edit” is usually a version that is around three and a half minutes, which is the usual sweet spot for playing on regular radio shows, meaning not those shows in which the DJ is mixing songs as if it was a performance in a club. For the latter scenario, some labels and record pools release so-called “Mixshow” edits.
(2) In addition to the above, “Radio Edits” could also be songs that have been censored to eliminate swearing, due to restrictions imposed by radio communications agencies (in the US, the FCC has long had a list of such words; you can check a terrific comedy routine on this that George Carlin did decades ago).
(3) Meanwhile, record pools also offer a variety of shorter versions, edited by contributors to the pool. These include, for example, so-called “Cutdown” versions, which reduce the length to within a range of three and a half to four minutes; “Short Edits,” which can be anywhere between about two and a half minutes to close three minutes long; and then there’re also “Super Short Edits,” which can range from about a minute and a half and just over two minutes, although I’ve found them as short as one minute. These edits are especially useful for mobile DJs who want to satisfy the dancers with a bit of a famous song, or a song that would be a good transition.
(4) Clean Intros, variously called “Clean DJ Intro” or “DJ Intro Clean,” are edits of usually mainstream songs that when the single, album version, or Radio Edit was\were released, didn’t contain at least an 8-bar long Intro that a DJ would use to beat match and transition from one song to another in a far easier way than otherwise. These versions have also been censored. However, some pools offer Clean DJ Intros where the Intro is 16 bars long. Usually, the song will also have either an 8 or a 16 bar intro.
(5) Dirty Intros are similar to #4 above, except that the original use of swearing language has not been censored.
In the original version of this response I had included some tips for creating your own edits and more, but this message is already very long.
Hope this helps. 😉