Chosen Solution

When searching for the right battery for my MacBook Air, I came up with two different models. A1369 printed on case and A1405 inside printed at bottom of battery. Is there a difference to which model to follow to get the right battery?

Go for the A1405. That code is unique to the battery, and so getting another battery that has the same code ensures capability.

I have a 2012 MB Air 13 and I replaced the original with an A1496. Considering the fact that the 2011 and the 2012 use the same battery, the A1496 might be a better option.