I'm assuming that you are talking about 1oz silver rounds and not silver bars. Yes, due to the different thicknesses, the diameter of a silver round can be bigger OR smaller than an ASE. I have silver rounds of all different diameters. But they all weigh 1 troy ounce. For example, older Monex silver rounds are well known for looking significantly smaller than ASE's due to their increased thickness. But they contain the exact same amount of silver.
There are also fake silver rounds out there that may be bigger or smaller because the manufacturer tried to make them weigh 1 troy ounce. So be on the lookout for those as well.