If Papias is not referring to our Mark or our Matthew of the gospels of the Christians Bible, then who are they ( Mark and Matthew) that Papias was referring to? In short, Is Papias of Hierapolis not speaking about our Mark and our Matthew of the gospels of our Bible? I hope you understand my question.
The answer to your question is very simple. No! There is no evidence whatsoever that Papias is referring to another Mark or Matthew. Ehrman is pretty much making things up here for reasons he will have to explain. Ehrman is strongly motivated for whatever personal reasons I cannot say, to destroy the faith of Christians in the inspiration of the Bible. In this case, he is really just putting out a lot of rhetoric. The fact is that all (and I mean all) of the early Christian writers believed that the Mark who wrote Mark is the one identified in the New Testament and that the Matthew who wrote Matthew is the one identified in the New Testament. There is no exception to this. Period.
Now, it is possible to claim that it was not Mark who wrote Mark or Matthew who wrote Matthew. I do not agree with this, but one can reasonably doubt that the biblical Mark wrote Mark and the biblical Matthew wrote Matthew, but to claim that it was a different unidentified Mark or a different Matthew is to simply make stuff up. What Mark are we talking about? Do we know where he was from or when he lived? What Matthew? And how do you explain that, if this is true, then Papias in literally the only author who believed this. Really, this claim by Ehrman is nonsense.
You did not tell me his supposed evidence. You did not tell me what Ehrman’s supposed “very solid reasons” are. If you want to share them with me (which of his books and what page number, either that or simply write back and tell me his reasons), that would be great, but in the absence of this I can say with great confidence that Ehrman is flat wrong on this one.