This is the sort of issue that arises from imprecise definitions as appear to be preferred in the UK. According to one source, medium eggs are 53-63 grammes in weight and large ones are 63-73 grammes in weight. Thus you can have a large medium being equal to a small large - in which case the answer to your question would be: "They are the same" - clearly absurd. I once asked at B&Q what weight their large bag of sand was (that was all shown on the bag: "Large", no weight, nothing) and nobody could tell me. It was the only size they sold at the time and I thought it was quite small.
I much prefer the straight forward weighing or measuring of everything, so in your recipe it should say X dl (decilitre) of egg white or something similar. Not too much to ask is it - or perhaps that would be too simple.