I used to be really big into Axis & Allies (and the rest of the Game Master Line along with Adjacents [such as War of the Ring...etc] that utilized A&A like systems).
The 1e A&A game was a typical wargame made by Larry Harris. It used the components common to Wargames of the time.
It was picked up by MB and they made the 2nd edition of A&A (the box that you have), though there were several printings of it (harder to tell which printing one has then what edition). It had plastic pieces for armies and other improved components as well as slightly simplified rules.
The Third edition was the Revised edition and made several changes to the rules.
Then, I think is when Anniversary Edition came out and then the first 1942 version (or was it 1941). That later one was sort of controversial for me as they stopped including paper money with that one.
Then came the revised 1941, the 1942 Second Edition, and more recently the rereleased Anniversary edition.
My favorites are probably Anniversary Edition, and then the Second Edition (Which you have) followed by the 3rd Edition.
That said, I'll always play a Game of A&A, but depending on who it is with, it will either be bonkers (as experienced A&A players use strategies that some would consider...unnatural in how the war normally seems) or more relaxed and enjoyable.