I thought that the undercoat/guard-hair structure was what distinguishes “fur” from mere “hair”?

I used to own a rabbit, with the classic “rabbit grey” coloration — that is, he looked like a wild rabbit, albeit twice the size. Both his outer fur and undercoat had multicolored hairs, so that blowing into his fur revealed an impressive “bulls-eye” of (iirc) 4 colors.