What's the difference between them? Is Quest an upgrade to Squiffy or they are different engines?

Entirely different. Squiffy is for making CYOA or hypetext games. The player gets a set of choices at each point and chooses one.

Quest is for text adventures, where the player can interact with objects and moving from room to room, traditionally by typing the command, but also by clicking. Quest will handle CYOA games too, but it is not the best tool for that type of game.