Both, "ausschalten", and "abschalten" are synonyms in general as well as in technical usage.
In colloquial German however nobody would say "ich schalte den TV aus". Nearly all people I know put it like this:
"ich mache den Fernseher aus"
or, to their kids
"macht bitte den Fernseher aus".
It may be that from this colloquial usage "ausschalten" is more often used than "abschalten".
As the nouns "das Ausschalten" or "das Abschalten" should be sufficient for describing the act of switching off, more complicates versions like "Ausschaltung" or "Abschaltung" were created without adding more information. The term "Abschaltung" is preferably used in context of nuclear plants.
When using "Ausschaltung" there may be confusion from it's other (euphemistic) usage in the meaning of eliminating opponents (best seen in the frequent usage during war times in a Google Ngram)