Before any of us were born, test were performed on different antenna systems. It was discovered that the maximum antenna gain possible for a single monopole was with a radiator, .64 wave length long. Broadcast stations have been using .64 wave length for DECADES.
In the CB market, we had 1/4 wave and 1/2 wave antennas. It was easier for the intended market to understand a 5/8 wave. Eccentially, it is the same as a .64 wave. As it was correctly pointed out by Doc, it's .625 vs .640, or a difference of .015 wave. As Bob correctly pointed out, that's about 6 to 8 inches.
To answer your question, and this was proven back in the 1930's, the MAXIMUM amount of gain possible is with a .64 wave length radiator. After that, the bubble breaks and the signal pattern becomes "distorted". So its clear that a .640 wave has more gain than a .625 wave. How much? Nothing to write home about. I'd guess you would be hard to measure it.
When the I-10K first came out, I spoke with Jay about using .64 in his calculations instead of .625 (owners will know what I'm speaking about, its in the TUNING SECTION of the manual). He said you could do that, but why?
My unscientific reasoning for sticking with .625 is that it buys me a little margin before breaking that bubble. For argument sake, what if you messed up your measurements and were at .65 wave? You broke the bubble!
This is picking a knat's ass, but those hose clamps add to the surface area of the radiator. Is it enough to constitute .015 wave? I don't know. Best to play it safe with .625 wave and not worry about breaking the bubble.
For the hardcore people out there, you need to adjust your radiator while watching the field strength, and re-adjusting for best SWR as you go. At some point you will see a peak. That's where you want it! Of course, Jay already did that for you which explains why it took 4 years for the production model to come to market.
This is not a perfect science. General rules apply. There is essentially NO difference between .640 and .625 (5/8).
The Wolf .64 antenna is a loaded antenna fed by a gamma match. That's 2 strikes! I hear he is a great guy and builds a good antenna, but it is still a loaded, gamma fed antenna.