Also worth considering is whether a recording is considered a "cover" if the writer (or one of the writers) is recording it with a different band (or solo).
The way I see it, after the original (or first) release is issued and another band began their recording *after* its release, it's a cover. If the song was given to two artists by the writer (who always has first selection rights as to who records and releases the song first), with one coming out before the other, but the second band not having heard the "first" recording, the second recording was not influenced by the first, it's not really a cover (in my opinion).
An example of this would be The Beatles recording of "How Do You Do It." George Martin found the song, had The Beatles record it, but since band didn't want such a sugary song as their first release, they didn't issue it. Martin then gave it to Gerry & The Pacemakers, who released the "original" version. Neither The Beatles' recording, nor G&TP's, was a cover of the other. Any recording made after G&TP's release IS a cover. The Beatles recording was later released on Anthology 1.
Now, if the writer (or possibly a member of the original band) records a second version of his/her song either solo or with another band, then it's not a cover. Or, if the writer never recorded or released their version until *after* the first release of the song by someone else, it's still not a cover (in my opinion, because it's the writer's song, first and foremost).
1984 recorded (but never released) "Step On Me" (May/Staffell).
Smile recorded (and released it much later) their version, but since May and Staffell are in Smile as well as being the writers, it wouldn't have been a cover if they'd all be released at the time of recording.
Same thing with "Doing All Right." Smile recorded their version, it went unreleased until the '80s, but Queen (obviously with Brian May) recorded and released their version. This recording, to me, is neither the original recording, nor is it a cover. It's simply "Queen's version." Same with "Polar Bear."
A none Queen-related example is "Because The Night," by Bruce Springsteen And Patti Smith. Basically, it was a Springsteen song meant for Darkness On The Edge Of Town, he recorded a version, but gave the song to Smith, who tinkered with it and released her own. The Springsteen version eventually released on The Promise is not a cover.
So, for me, in the end, the writer or co-writer of a song is never covering *their* song, even if it's released after.
As to something like Roger Taylor releasing his live recording of "I Want To Break Free," which he didn't write but was a member of the band who first recorded it, for simplicity I tend to lump that into the "not a cover, but their related version" category.