Roughly yould could think of cca (if you could compare them) as how good is the battery at a short high current draw. The Ahr rating how long could you have a low current drain until the battery is discharged. Cold is a worst case as the chemical reaction slows down.
dduelin hit it well above, but to put things in a little different wording- you are actually comparing apples to oranges, as in two different types of batteries. There are two main types of automotive (I'm including MC batteries in here, since they are similar, just smaller) batteries- starting, and deep cycle. Starting batteries are just as the name implies- they are used to start the vehicle, then (unless there are issues) are topped off when the engine starts, and aren't really used again until the vehicle has to be started again. The alternator provides power as we ride, except for brief moments where the battery might act as a capacitor when there are short, high loads that might overpower the alternator. They aren't meant to be drained a lot, then charged back up. Each time a starting battery is drained low, it vastly shortens it's life. A deep cycle (commonly known as a marine battery) is made to provide a slower rate of discharge, usually for a trolling motor or RV backup battery when the engine is off. They can be drained low and recharged many times.
The CCA rating of a starting battery is the best rating for that type of battery. It uses a constant temp, and a cold one- where a starting battery has to work the hardest, to equal the playing field. An Ahr rating is for a deep cycle battery, which is subjected to repeated discharges, and is best rated for how much current it puts out over time.
For battery ratings, they are just a rough guideline at best. There has to be some way to compare them, so CCA is used (for starting batteries). There are lots of other factors though, such as the actual quality of the battery. Just because two batteries might be rated at 220 CCA, it doesn't mean they will last the same length of time. Its like comparing car engines- two 250hp engines that get the same fuel mileage won't necessarily last the same amount of time...one might go for 100k miles, the other for 300k.
As for comparing a replacement Yuasa to the ones that came in our bikes, I'm of the strong belief that they are indeed different. I can't say whether they are actually different designs, or just built to different tolerances, I think the long history reported on this site alone has shown the difference. Most OEM Yuasa's seem to last 4-6 years, while replacements get 2-3 years. Even if they are made on the same assembly line to the same (supposedly) specs, they may well be a different quality. I used to work in the bearing business. Our company made precision bearings for many uses, including military, aerospace, and computer hard drives. Sometimes the very same bearing, including the same part number, could be found in military components and a household appliance. Whats the difference? When they are inspected, the best of the best, held to the best tolerances, go to the military; the stuff that doesn't pass for their use gets packaged for uses that don't require the same precision. Obviously the military grade bearing will work better and last longer. I suspect our batteries are the same way. They may very well came off the same assembly line- but while the best of the best go to be assembled into new bikes, the ones that weren't quite as good get sold as replacements. That would easily explain why replacements seem to last less than half as long.
I'm in need of a new battery...my 6 year old OEM is failing. If I could get the same battery, that would last another 6 years, for $150 or even $175, I would gladly pay it- just for peace of mind that I won't have to worry about it for several more years. But since history has shown I won't get that kind of life, I would rather spend half as much on a battery that will most likely (again, going by reports on this site) last just as long as a replacement Yuasa. I'll probably be contacting Two Brothers for my replacement.
Jim