What is TAR?
TAR does one job: it glues many files into one, preserving Unix permissions and structure. It compresses nothing at all, which is why it is nearly always paired with gzip. It is the standard way source code and Linux software move around.
What is TGZ?
A .tar.gz - or .tgz - is a TAR archive run through gzip as a single stream. Because compression sees all the files at once rather than one at a time, a folder of similar files usually ends up smaller than the equivalent ZIP. The trade is that reading one file means decompressing everything before it.