The cute one is the uke, the cool one is the seme, which, coincidentally, tends to be expressed in anime through eye shapes: cute characters have tareme タレ目, drooping eyes, slanted upwards, while cool characters have tsurime ツリ目, slanted downwards.
He's generally the more feminine character of the two, the shorter, weaker, more timid one, maiden-like, whom the seme, as the 'guy' in the relationship, would protect or court.
The ships fujoshi ship are typically heteronormative: the uke is the 'girl' of the relationship. The term fujoshi 腐女子 means 'rotten girl.' It's a self-deprecating label used by girls into gay shipping: just like weebs call themselves degenerates, fujoshi call themselves rotten, in the sense that they must have a rotten brain to have all these perverted gay shipping fantasies about characters from stories that don't feature gay characters to begin with. Character: Koganuma Minori 古賀沼美埜里 Anime: Outbreak Company (Episode 4)