A minimalist wardrobe is a philosophy rather than a method. The goal is fewer possessions; how well they combine is a separate question.
This is the distinction that matters in practice. A minimalist wardrobe can be badly matched, and a capsule wardrobe can be fairly large. Owning twenty garments that go with nothing is still a wardrobe with nothing to wear.
Choose it when the volume itself is the problem. Choose the capsule method when the problem is that nothing goes together.