Take Kodak ASA 400 Tri-x and their ASA 400 Tmax B&W films, completely different grains. Same goes for Ilford, since they have more types of film you can even take the fine grain Delta 400 and the not much (if even) finer grained ASA 125 FP4. This doesn't make one film better than the other, I for instance prefer the general look of the bigger grained FP4.
Grain size wise the Kodak T-grain probably was the biggest revolution in grain size during the last few decades, you can still debate if it produces the best films, many different views on that here on APUG
To some extend the developer influences the grain as well.