Yeah it does; 12 vs 16. I guess that might be the explanation.
It's not, reinforced club just has better strength scaling than claymore does. Unless they changed it for the PC version, claymore has 53 scaling at +5, but reinforced club's at 78. There's the full list at
http://darksouls.lljk.net/1.04/weapons if you don't mind spoiling yourself on the available weapons, though that's for the console versions so it's at least a little out of date by now. Should be good as a rough guide at least.
It'd be kinda dumb if the bonus from scaling depended on the minimum stats to use weapons. Some of the heaviest ones take 40+ strength, they'd end up outclassed if the lower requirement weapons got better scaling.