I have a few pairs of Marc by Marc Jacobs from a couple years back and none of them said "by" on the box, I don't think?
I have some Marc by Marc Jacobs with "by" on the box. I can't remember if the ones with "by" on the box are new or old and I'm not home right now so I can't check (I *think* this season's shoes have "by" on the box but I'm not certain). But yes, some have MARC JACOBS on the lid and others have MARC BY MARC JACOBS on the lid. The shoeboxes are always white lid/black box, though.