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.
What is ZIP?
ZIP is the archive format every operating system opens without being asked. Each file inside is compressed on its own, which is why you can pull one out without unpacking the rest, and why it compresses a folder of similar files less tightly than formats that treat them as one stream.