Mmm. I suppose the easiest way to put it would be the intent and a single ingredient. If OP made it to be wheat pasta — some recipes do call for egg (usually just yolk) — then wheat pasta is what it is. Though, of course, you can find recipes with just wheat.

Egg noodles (the recipes I'm familiar with) require more eggs than wheat pasta does, and typically uses the full egg and not just the yolk (ones calling for just egg white are few and far between.)

It's a pretty semantic difference when you write it out (though this argument could go for ALL noodle forms), but it's a big enough one in practice where it could completely alter the flavor profile, consistency, and texture of your dish.