The GI is a replica of the 1911 carried by GI's in WWII.
The Mil-Spec is based on the current 1911 US military spec which includes a few changes after WWII. Someone else can detail differences from the GI model.
The "loaded" model includes a few of the common after-market upgrades that many 1911 owners add to their 1911's such as Novak sights, beaver-tail grip safety, ambidextrous thumb safety and extended safety levers. The SA website lists all of the differences between the loaded model and the Mil-Spec model.