An assistant gives advice or instructions (the little animated figures that pop up in Microsoft programs, for example), whereas wizards walk you through a process (configuring printers, creating a letter or invoice, etc.) step by step. Hope that helps!

Just to expand my comments to Laurent.

Certainly under Windows, an "Assistant" tends to be context-dependent, so that annoying paperclip will pop up when you type "Dear" in Word, with it's "I see you're writing a letter" crap. It just helps with a single 'aspect'

A "Wizard" is for a whole process - as Laurent says, printer set-up, software installation, also more mundane stuff like Extraction Wizard for zip files, as soon as you take the first step in the process. It also has preconfigured standard options ready selected, which you can sometimes change.

It may also be worth pointing out that another key difference is that you can turn the Assistants off. Whereas you can't by-pass the Wizard :-) Well, I daresay you probably can if you know exactly what you're doing, but I would think that most of us would struggle to use Windows without the Wizards, but can cope very easily without the Assistants.