It may not be correct, but my idea of an all-rounder stems from the rise and rise of single species specialist angling. Once upon a time no one started out in their fishing life as a carp or barbel angler, now a fair few do. They don't have the background in angling that many of us benefitted. There are people out there that have never fished with a float.
Therefore, my idea of an all-rounder is anyone that is more than a single species (single method?
) specialist. However, a carper that has the odd dabble on a winter river for barbel doesn't really count. Matt Hayes and John Wilson are probably as good an example of all-rounders as you'll get. However, as far as I'm concerned, the fly and sea fishing isn't required to be considered an all-rounder.
If you can fill a fairly substantial sized room/garage/shed with gear (that isn't all duplicated hording or matching doubles/triples), you are probably are an all-rounder.