I haven’t posted a Troublesome Pair for ages but I’ve had this one up my sleeve (erm, no, I haven’t, that would be disgusting!) for ages and hadn’t got round to posting it. With a Birmingham Cough going the rounds still, this seemed a seasonal post; my apologies to the more sensitive reader. It is a valid and troublesome pair, though!
Mucus is the noun, i.e. the thing itself: slimy stuff that gets secreted by animals and even plants (it’s more commonly known as mucilage in plants, though mucilage is also, in general a viscous bodily fluid or secretion).
Mucous is the adjective – so mucous membranes secrete mucus, for example.
Bonus word: mucilaginous is the adjective that goes with mucilage. I bet you’re glad you asked, aren’t you!