I didn't coin the phrase; that's how it was described both by FN when they marketed it and by NATO when it was standardized in 1980. But OK.
SAP, if you want the Brassey textbook definition: "Steel-tipped bullets give better penetration than conventional jacketed bullets while falling far short of the performance of armour piercing bullets.... The 5.56 x 45mm SS109 round has a steel tip beneath the envelope ['jacket' in N America] and ahead of the conventional lead antimony core. These high velocity bullets will pierce mild steel plate at relatively short ranges, but their main purpose is to overcome the protection afforded by helmets and body armour."
Straight AP rounds often contain a tungsten core and tend to be considerably more expensive. If the weapon system is intended to take on armoured targets, AP or API becomes worth-while, but it's over-priced for most uses.
In context, the Yanks had pushed a .30 cal round on NATO in the 50s. When they got to Vietnam, they found that their M14 wasn't optimal and went for the AR-15 (initially taken up for USAF security) for general usage. Post-Vietnam, they elected to stay with the M16 and 5.56 x 45mm as their standard and had the clout to get NATO to go along with that.
It was however still in the midst of the Cold War and NATO's main concern remained the Fulda Gap. Given some indications that Mr Bear might give his troops body armour, NATO, while saying Yes to the smaller round, elected for something better able to penetrate Soviet individual protection than the then-standard M193 round. A NATO competition was held in the late 70s; the Belgian SS-109 SAP round was deemed the winner and accepted as NATO standard. (It will, as it happens, penetrate a NATO target-definition helmet at 600 metres.)
Second bit of trivia - one of the other contenders was a 4.7mm German round. It had decent enough lethality, but bore erosion was a killer and the Yanks had invested a pocketful of change in the 5.56mm one, so it bit the dust.
The longer bullet in the newer version required a different rifling spin than the older one for optimal stabilization, so the standardization of a specific load (as opposed to just the cartridge) was required if the concept of NATO interchangeability was to be maintained.
