The head resembles a Barbasol, which IIRC was made by 'Conrad' or some such outfit. Of course swapping out handles is simple compared to designing and tooling for a different head. Here is the 'non-floating' head of my Barbasol:
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Groove count is ten on both heads. The handle on the "Gillette" might or might not be the handle it had when new.
I did get at least one good shave out of my Barbasol. From a conversation with a B&B friend: "Turns out that the non-floater did a fine job with good prep and good lather."That does look really similar! The whole razor seems like the same tarnished uncoated brass though, so there's at least that difference, and is one of the reasons I wonder if head and handle were originally one razor.
How does that Barbasol razor shave (that is, in terms of aggressiveness, etc.)?