Looks like a HD to me, but the case may not be original and yet a nice case. If it opens and closes nice and smooth, go for it. There was an uncased HD on the BST going for $35 (a very good deal) recently and I've paid $80 for a *nice* HD in the correct case. So somewhere in between.
The case could be a number of razors though. My blade cases are closed without the cutout in them. That case was used for quite a few different models. ( Check out Achim's site www.mr-razor.com )
So it's not a matched set, the razor ( 50s ) is not as old as the case ( 30s/40s )