I've tried hard to find a difference between the two, and the only thing I found is that you can add a hardener to Hypam, but not to Rapid Fixer. I must admit that it's a bit weird to have two such products (why not sell only Hypam but call it "rapid" ?). Maybe we could get Simon R. Galley from Ilford to chime in.
several years ago this question came up on the Ilford site and i talked with their tech support people; who at that time told me that the production of the fixer had been removed from the US and the product was being made in England and they went back to using just one standard name. It seems that in the UK it was called Hypam and in the US Rapid Fixer.
Since this information came from someone at Ilford I had no reason to doubt the source, however, perhaps Simon can add or correct this information.
A look through the 'fact sheets' on the Ilford site shows that both have the same characteristics, mix rates, fixing times, etc. Only difference of note, you can use hardener in Hypam, but not in Rapid. Hypam is packaged in large sizes and Rapid in small sizes. Curious thing, though, in the one size they have in common (5 Litre) the Rapid is much more expensive.