I have trouble keeping track of which plants we are talking about when we talk about Monkeygrass. Here’s a list for my future reference and maybe it will help you too.
Mondo Grass with thin leaves- Ophiopogon japonicus, shorter and thinner leaves than standard Liriopes
Monkey Grass (Standard)- Liriope muscari- purple flowers
Giant Monkey Grass-Liriope gigantia
Aztec Grass- Liriope muscari 'Aztec'- bright white variegation
Variegated Monkey Grass- Liriope muscari ‘Vareigata’- variegation is more yellow/gold
Dwarf mondo grass- Ophiopogon japonicus ‘Nanus'- very very short and not very drought tolerant
Black mondo grass- Ophiopogon planiscapus