The battery from the Mid-2009 version is labeled A1322 and has the APN 661-5229. It is 10.95 V and 60 Wh.
The battery from the Mid-2010 version is ALSO labeled A1322 and has the APN 661-5557. It is 10.95 V and is bumped up to 63.5 Wh. It is fully compatible with your machine.
As for iFixit's parts, these particular batteries are pulled directly from new or refurbished Apple machines. We mark them "used" because they came from a machine that was turned on for testing (much like a new car becomes a used car the second it is driven off the car lot). The mAh rating is represented on the part page as a range rather than a specific number, because these batteries, direct from Apple's machines, have a sizable variation in actual mAh from battery to battery.