Frugalism doesn’t mean you don’t like and appreciate high-end items. I have a Michael Kors wallet and purse that I absolutely LOVE! But, they came from the outlet mall, and I got them as a Christmas/Birthday gift (January Birthday up in here).
Minimalism can be whatever you need for you. It can be a capsule wardrobe instead of 2 pairs of underwear, one pair of shoes, and three t-shirts. It can be one set of 4 pots and pans instead of 12. There are no absolute rules.