From the looks, they're the same hood.

 

Specifically in the STI lever hoods? Is there is a difference? I need replacement hoods and have 6500 levers with one button Flight Deck buttons on the hoods.

I don't know what the difference is, but I just replaced my hoods on my ST6500 and when ordering I found that the hoods for 6500,6501 were the same part number and the 6510 were a different part number. I got the ones that said for 6500, 6501, and they fit fine.

 

I think the nameplate caps are different. The 6500 was the one that rattled, so they fixed it with the the 6510 which has the shiny chrome nameplate and no rattle.