When Nox loads, and the player has a choice of single player or multiplayer, there are two single player options - "Solo" and "Solo Quest". What is the difference between the two?

Solo refers to the single player campaign, whereas Solo Quest is a series of levels/dungeons/challenges that act kind of like an offline multiplayer mode of sorts (sorry for the confusing comparison),

Yeah, the options are a bit confusing, but new players should choose Solo – the first chapters explain quite a bit about the mechanics of the game.