The Government Model is the same pistol as a "GI", it goes back to the early days of production when colt was producing pistols for the government and also for the public. The term was simply used for marketing, so I'm told. The only differences between the two are markings and finish, depending on the era. "GI" is simply a term applied to most pistols that are either wartime issued pistols or modern repros. "Milspec" could apply to either, usually from what I've seen it is in reference to modern basic pistols with a military-type finish (ie Springfield's version). A more accurate use of the term might be any pistol that isn't a hand-built custom target or competition gun. Just my opinion, if I'm wrong I'm sure I'll be corrected.
A Commander length pistol has a 4.25" barrel, and a slightly shorter dust cover than a Gov't Model.