Any dimensionality reduction method (DL-based or otherwise) can be viewed as a form of compression. But, the end goal in data dimensionality reduction is usually quite different than with data compression.

Either way, this is much different than model compression/distillation, which is compression of the parametrized functional mapping itself. As a silly example, imagine you fit a 100-degree polynomial to noisy linear data using some proper regularization. You would find that can distill/compress your 100-degree polynomial model into a 1-degree model with comparable accuracy.