In Over the Edge or The Warp System is there a difference between having a 2d trait and not having a trait?
The only time you can have a 2d trait is for unusual or technical traits at Superior grade (or a Good grade unusual & narrow trait, if the optional "Narrow Trait" rules are used). Such traits cannot be used by people without the trait at all, as the average grants 0 dice. (WaRP SRD v1.0, p. 5)
Not having a common trait gives you 2 dice (an Average rating), while anyone who actually has that trait will have it at Good or better, giving them 3 or 4 dice.
So the difference is that a 2d trait necessarily means that it is a specialised skill that cannot be used "untrained", and that the character in fact is fairly accomplished at that specialised ability. Meanwhile, having no trait – but still 2d – means you're trying to do something that anyone can manage without training, like throwing a ball.
Note that a character doesn't count as having a trait that is rated at Average. The traits that are relevant to a character and written on their sheet will always be Good or better.