AIR 3.6 apk : different version on Google Play and AIR 3.6 SDK Official

Are you sure about those numbers? Usually the format is like 3.6.0.5990, where the first three parts are the version number, and the last one is the build number. It's not surprising that the release version has a later build number than the one currently in the Google Play store.

I checked by the way, and Google Play does show 3.6.0.597. It's possible that in the four digit build number the last one is always zero (it seems to be), and that there were two further builds between when the Google Play one was submitted, and when the current SDK was posted.