They are manufactured by different companies. The basic architecture is the same, but there are just slight differences, such as the standard memory (DDR2 and DDR3), and other items like that.
I feel obligated to mention that it probably isn't worth your money to be purchasing a new graphics card for that old of a system. I did the same thing to an older system a while back with similar specs. All it did was whet my appetite, and less than a year later I was building myself a whole new system. I would save my money to build a new system or buy and upgrade a new system.
That being said, if you choose to upgrade your video card, I like this 3850 model: http://www.newegg.com/Product/Product.aspx?Item=N82E168.... That is the first one mentioned of the 3850s. The performance difference between the 3850 and the 4670 is negligible, and the 3850 might in fact be a better option for your older system than the 4670.