The TCIII to my knowledge only is made in a 18''
The wheel was designed with the R35 in mind because the the brakes have clearance.
The Advan GT has many more options. This wheel is made up to 20'' and also was designed with the R35 in mind.
The wheels have the correct off sets for the R35 and are manufactured up to 12 '' wide. This is the wheel I have on my car.
Both are great options. The Advan TCIII would be a nice choice for a track focused GTR where the owner would like to run slicks, or someone who would want to put drag radials on their car for high powered roll race R35's