1. They are not even remotely the same nor are the compatible, nor do they use even a compatible or similar connector. Completely different, in no way inter-compatible.
There ARE two separate USB 2.0 internal headers and but one of them supports a full USB 2.0 9 pin connector that is capable of supporting two full USB 2.0 ports while the other is a single 4 pin USB 2.0 header located in between the memory slots and the USB 3 9_10 header next to the edge of the motherboard. That USB 2.0 header requires a half type connector. You should still be able to use either type of connector on either of those USB 2.0 headers so long as you line up the correct line of holes with the correct line on the connector that matches the number of pins. On the larger one for example there is a row with five pins and a row with six. If you were to use a half connector on that header that has only four holes you would want to use the row with only four pins. Since these pins are exposed it is not necessary for the WHOLE connector to be entirely keyed the same.
The larger one is actually two separate USB headers and if necessary, unless the device you are wanting to connect to the USB_3 header MUST be a full 9 pin connection, it should still work.
Better might be, if you are uncertain about your options, to simply get an add in USB 2.0 expansion PCIe card and use that. Cases and devices that require USB 2.0 connections are becoming more and more uncommon and it is rare to see one these days on any premium aftermarket product that requires anything less than a standard USB 3.0 connector so finding USB expansion 2.0 cards or boards with many USB 2.0 internal connectivity options is only going to grow harder and harder.
Why, exactly, do you need to connect a USB 2.0 internal header to the CASE? Is this to enable front panel USB 2.0 headers? If so, simply don't use them and just use your internal USB 2.0 header for your AIO cooler. You might have to instead use or get a rear panel USB 2.0 port for anything external you want to connect 2.0 devices to, or simply use on of the other external rear facing USB headers, all of which are backwards compatible and will work fine with any or at least most USB 2.0 external devices such as keyboards, mice and headphones. Or, you can get a cheap USB 2.0 hub and expand one of your rear USB 2.0 ports into several more if need be.
In any case, I don't see it being necessary to connect your case to an internal USB 2.0 header unless there is something you have not mentioned or I am missing. The cooler, obviously an older model, different story but between the two headers you have on that board one of them should work fine for that AIO.