It’s easy to claim the titles of mother/father or mum/dad, they’re a biological thing or even a role demarcation. You are, or you are not, a mum or dad.
Being a parent, on the other hand, is a different kettle of fish. You can be a mother or father without ever actually being a parent. To be a parent requires a person to actively parent – to guide, nurture, hold, love, support, cherish, discipline, nourish and be present to a child. Not all at once and not all of the time, but certainly a significant portion of it.