My research indicates that a revised edition may have error corrections made on a piece that didn't really sell in the first place.
It might make a difference if we are discussing a short story (which seems to be much of what folks here write) or a book.
For a book, my research shows :
a second printing is additional copies printed without any changes;
a revised edition is subsantially the same, but with minor corrections, and is used when the original printing did not sell well;
and a second edition has more substantial changes, and / or the first printing sold well.
For example, the Hardy Boys books were originally written in the 1920s, then edited in the 1950s to included what was then modern investigative procedures, such as fingerprinting. I am pretty sure the edition number was incremented with the updated version. If those books were updated again, the edition number could be incremented yet again, for how ever many updates.
Editions other than one are probably more prevalent among non-fiction works than fiction. Usually a fiction book is not changed other than SPaG. The Hardy Boys is the only fiction example I can come up with. I thought it would do as an example hopefully many reading this know.