Ya they should, it says S&W j frame round butt and the back of the 638 goes up like a centennial. I think I may have to pick up a purple pair for my wife. If you do get them let us know how they work out.
I don't think they'll fit. A real J frame grip is quite different than the molded, one size fits none grip of that abomination now called a Bodyguard. You may want to call Hogue to make sure before ordering.
Pointshoot, S&W makes three very different guns called Bodyguard. The 638 is just one of them. The gun shown in the OP's first post is not a 638. Follow the links.