So, there are multiple factors that go into catching a Pokemon. The stats of the Pokemon itself, berries, how many throws you"ve done (i.e. decreased difficulty with each throw, and in increased flee rate), potentially curveballs, the ball you use, and the catch ring.

Firstly, the balls decrease the difficulty, the Basic Pokeball being the base level, then the Great Ball, and the Ultra Ball decreasing the difficulty of the catch (premium balls are a different thing, so we can exclude them).

Secondly, there is the catch ring. You can get a Normal catch (no bonus), a "Nice", "Great", or "Excellent" catch, which also decreases the difficulty of capturing the Pokemon with each one, respectively.

How do these coincide with each other? Is it like a 1:1 bonus, or does the Pokeball type, and the Catch ring bonus affect the catch bonus differently?

E.g., does getting a "Great" throw with a Pokeball equal the same bonus as getting a "Nice" throw with a Greatball?

Full article