I'd say you are right on both statements.
When you develop longer, more metallic silver grows... thus more grain.
Literally ISO never changes, but that's just a nerd's fact. Call it exposure index when it's not "standard"... EI can be set higher on your camera if you develop longer. That's pushing.
When you develop less time, the difference between the clear and the darkest parts of the negative isn't as great - because of the same reason... the metallic silver hasn't developed as much.
The difference between dark and light is contrast, so that's why less development is less contrast.