What is TAR?

A tape archive, and it does exactly what the name suggests: bundles files together in order without compressing anything. On its own it saves no space. It's the first half of nearly every Unix archive, and what build pipelines and Docker expect to be handed.

What is TGZ?

A tar bundle compressed with gzip - the standard Unix archive. Because gzip sees the whole bundle at once rather than each file separately, a folder of similar files compresses better than the ZIP equivalent. The catch is that reaching one file means decompressing everything before it.