(Also, you don't need apostrophes in your subject.)
A woodcarver makes wands and staves. A carpenter builds or repairs a house or furniture.
I'd like to revise my answer after some thought.As others have explained, there is a difference. In the context of D&D, though, I wouldn't sweat it: if a character with Carpenter's Tools proficiency wants to do some decorative carving, I'm not gonna say, "No, you can't, you need Woodcarver's Tools proficiency for that."