I think both are used to edge - trim pathways, border planters, etc. Both can be invasive. My 'description' of monkey grass is that it's a thinner blade and usually pretty short 'fall' of grass in each clump. Liriope is a wider blade, taller plant and blooms with a more noticeable spike. I think the color is different too. Monkey grass is very very deep green vs Liriope a pale green or light green with white stripe. Monkey grass is sold as 'mondo' grass, I don't know where we stopped calling it that and started calling it monkey grass, it isn't even very agile! martha OH, thanks for the link to the 'horse nettle' photo. I think it's the same thing, but the flower photo looks big and lovely. These flowers are maybe the size of a nickel and not especially attractive.