Well, I recently replied to a thread about a fazer (combination hazer/fogger). It goes into pretty much detail about the difference between them. In short:
1) Fogger = produces a relatively dense fog/smoke (actually it’s more of a steam) that dissipates (short “hang-time”) pretty quickly depending on the quality of the fogger and the fluid. It is/was mainly ment as an effect. To be used from time to time during a show and only for a short period of time. While it travels up and away it does have the side-effect of emphasizing the light beams as they travel through the air. The smoke/fog is very visible to the audience and (more often than not) has a less than nice smell to it. It also uses quite a bit of fluid if plan to use it regularly during a gig.
Foggers need time to warm out and also to cool-down. So you can’t just drop it and start it.
2) Fazer = Closely related to a fogger, but has a ventilator for better dispersion and it created a thinner layer of fog. It can usually run continuously, so more practical for creating that atmosphere you want for your lights. Some of the drawbacks of a fogger also apply to fazers as they share the basic premise to operate.
3) Hazer = produces a very light mist of miniscule drops with a long hang-time. The mist (haze) is nearly invisible to the audience, yet when the light beams hit them they defract the light a bit, showing the beams very clearly and thus enhancing the effect your lights have. You can use a hazer permanently to replenish what dissipates. Hazer fluids are often oil-based and this can leave a light residue on gear, so place a hazer wisely. Also, it takes some time (up to 30 minutes) to get a nice even haze of the desired thickness up, running the hazer full speed. Once you are set, a simple 10-15% operation will keep it up. So plan ahead. Make sure you have your haze in place before the party starts. Especially oil-based hazers can be a tad noisy when going full speed.
Hope that helps some.