The industrialization of the American military in the 1940s during World War II pushed many new acronyms into the English vocabulary.
New technologies with complicated names often leads to the creation of simplified terms like RADAR, SONAR, SCUBA.
The military has been a major source of acronyms and abbreviations and that's true of these two. SNAFU: Situation Normal, All Fucked Up - a reference to the general chaos and horror of the battlefield.
FUBAR: Fucked Up Beyond All Repair/Recognition - like SNAFU, the acronym FUBAR dates back to World War II and described a thing or situation in which things were beyond hope - although in a wartime military setting that doesn't mean you didn't have to deal with it.