Masculine denotes "straight ahead"; feminine (derecha) is "right."

Well, right is also an adjective, so it can be either. So la mano derecha 'the right hand' or just nominalized as la derecha. But as a noun, yes: the feminine for the right hand and the masculine for the law. You could also have el lado derecho for the 'right side'. And besides a noun and an adjective, it's an adverb, as pointed out, meaning 'straight, direct (cognate), or upright'.

What's interesting is that Latin rectus 'straight; correct, (morally) right' was augmented with de-. And that Latin words dexter (related to Skt dakshina 'right; south'), as well as sinister 'left', lost out in Spanish. Derecha, izquierda.