No, there is no general convention, or international standard, or anything remotely like that. Even manufacturers that publish charts of how their pieces compare to other brands don't always agree with others. The problem is, every maker seems to measure things in slightly different places. For example, cup size can be measured at the very first start of the dropoff into the rim, or further down the curve, or at the place where the cup itself "starts".
People also come to different conclusions themselves about which piece feels bigger or smaller due to the shape of their own teeth and facial structure.
Even worse, some mouthpiece makers are notorious for huge variations in the sizing of their pieces. Bach is notorious for this with their mouthpieces. You can pick up 3C examples from the 60s, 70s, 80s, 90s, etc., and have them all vary wildly in size. In fact, sometimes they vary even within production from the same time period.
Most modern makers use CNC equipment to make them now and consistency is much better of course.
Another thing to be aware of is some makers use very similar labeling, like Schilke and Yamaha. They both might make a 13A4A, but they would actually be considerably different dimensionally.
The only real way to determine what you want to play is try them for yourself, unfortunately.