I think I have determined what differentiates a "bar" from a "pub" in Edinburgh: what men pee into. If it's a pub, you get a collective trough like this:
Whereas if the establishment has distinct urinals, they fancy themselves a "bar".
The Melville is definitely a pub, and a large one at that. Right next door to Bert's, this is an upbeat place that had no cask ales other than Deuchars. But they played good tunes from the '80s.