A wide attacking midfielder and a winger are two completely different positions. One is primarily based out wide, hugging the touchline and expected to provide crosses. A pure winger is an almost dead position.
Wide attacking midfielders tend to cut in, switch positions and provide goal scoring support as well as assists. They tend to make very few crosses and you often get right footers playing left and vice versa. This allows them to cut in field.
Moyes has played mata more like a winger so far which is why hes been nothing more than ok. He made more crosses in time at United than he had in 4 times as many games with Chelsea.
We have two proven attacking mids who we consistently play left wing. It never worked. Rooney is better than both from the left which makes it even more baffling.