The original MBA used 1.8" wide drives that were also 5mm thick, which is thinner than the standard thickness. They were PATA. They also used a ZIF connector, so those drives were not compatible with standard 1.8" PATA drives. The later MBAs used a 1.8" SATA drive with a ZIF connector as well.
RunCore makes SSDs up to 128 GB for them all:
Products | RunCore
They will cost you.
If you want to figure out which you have, Click the apple, "About this Mac...", "More Info", then look for the Model Identifier. MacBookAir1,1 takes PATA. MacBookAir2,1 takes SATA.