The AAZ pump was used on turbo diesel engines with "indirect" injection... fuel is injected into a pre-combustion chamber rather than directly into the cylinder. These are known as "TD" engines.
The AHU pump is used on turbo diesel engines with "direct" injection... fuel is injected directly into the cylinders. These are known as "TDI" engines... the D meaning direct.
Bottom line: having a turbo doesn't make it a TDI engine. The type of fuel injection used determines the naming schema.
The challenge is that there were a couple different flavours of the AAZ pump that can make it confusing, particularly when we can't crack open the hood and have a peek ourselves. In particular, there's a version that has significant electronic controls.... it shipped just before VW switched over to the TDI design.
Probably the easist way to know which you have is to look at the top of the pump. If the pump has a throttle cable it's an indirect or TD engine, most likely with an AAZ engine/pump. If there's no throttle cable its the TDI engine, most likely the AHU engine/pump.
In case it's not confusing enough, some folks take the electronic TDI pump and convert it to manual control. These are referred to as "m-TDI" pumps and are almost always home-brewed.
If all else fails, you might want to post a couple pictures of the engine and the pump. This is one of those times when a picture is worth a thousand words.
There's a sticky post at the top of this forums that explains how to do this.
Edmonton, Alberta, Canada
2001 silver TDI Jetta Malone Stage 1.5 , 2001 blue TDI Jetta SBIII 216s Malone Stage 3
1970 Bay Window bus
Gone but not forgotten: 1969/1971 Beetles, 1969/1974 Westies, 1979 Rabbit, 1986 TD Jetta, 1992 gas Jetta, 1994 TD Jetta
Here's a small collection of HOW-TOs