Clearly not! Although I don't know what the specific differences in linen type would be between these two garments in this case (or most cases of upper-middle class folks. The extant shirts that I have seen for common wear aren't all the delicate gauze you find on the Saxon Princesses, so it is possible that a decorative apron could be made of fabric from the same bolt as the undergarments came from...

Couldn't it...?