Unfortunately there is no standard size specification for split shot. For a good article see this link.
In the US the Water Gremlin size is the defacto standard because it is widely sold by Walmart and other retailers.
The diameter of a split shot is not important, but the weight is important in bobber fishing. For the best sensitivity the bobber should be weighted so that most of the bobber is submerged. The popular 3/4 inch balsa oval float made by Thill, Eagle Claw and others works well with a #3 Gremlin split shot.
I learned the hard way that one cannot depend on advertised sizes. I found a bargain source for split shot by the pound, and ordered a big supply because I lose a lot of them. I ordered size 3 and got a size somewhere between a 4 and 5.