I suppose not having to wear track pants, an early 20th century hat and cigarette are what differentiate the two.

It's the squat you'd use to use a toilet like this: https://bredlowfamily.files.wordpress.com/2011/10/toilet.jpg

From what I know, the slav squat is also an equivalent slang term. In gym and fitness contexts, it would be an ass-to-grass squat. The most polite way of expressing it would be to call it a deep squat, or a squat that's "past the parallel".