Ideas don't capture the full spectrum of ways we can live minimally. A few examples I've personally seen used are digital minimalism, materialistic minimalism and minimalism relating to relationships.
Rephrased:
Minimalism is removing things that don't work, and improve on those things that do.
I think for me ideas and things are about the same. But for people where that isn't the case then that is a good rephrasing.
I think it comes down to being able to curate your life to get whatever you feel is the best of the things around you.