I've only seen 'skater skirt' used recently. It seems to mean an above the knee skirt that is about 3/4 full.
There are a lot of named clothing styles that I don't feel like used to have names, or at least not names consumers knew. I have a theory about that. I wen't on a rant in the complaints thread about search technologies relying on words, and this is one example of how our reliance on an imperfect technology shapes us to it's limits.
When we shopped mostly in stores we never knew what clothing styles were called, unless they were really trending, or we read fashion magazines. When you used to go to a clothing store and you had a style of skirt in mind you could say "I want something about mid thigh, sort of full, but I don't want to look like a square dancer!" or "a nice vintagy dress, with a structured bodice, but a pretty full skirt" and a sales clerk could help you find it. Or it was easy to browse the racks and see what you wanted, particularly in more than one category at once (skirts and tops).
Online search tools are pretty bad at this. If you are on a department store's website there may be 300 skirts available. If you know what to type in that search bar you will be more successful. Some of them have pretty good filtering systems that allow you to filter by trait, but that trait will still be listed as "skater" or "fit and flare"
That said, google trends shows that 'Skater skirt' didn't gain traction until 2011, and is mostly searched in the UK and... The Philippines.
(Uk search index 92, Philippines 80, Ireland 53, USA 10.