You specifically mention the MK-678 and the MK-678G. They both have an adjustable rear sight and a 6 7/8 inch barrel. The difference is in the barrel WEIGHT.
The MK-678 has a TAPERED barrel while the MK-678G has a BULL barrel. That is where the 4 oz. difference is. You can see pictures of both models on the ruger web site.
I bought the bull barrel Govenment model because to me it looked cool. Others find it too front heavy and recomend the shorter 5 1/2 inch bull barrel. They say both lengths shoot just as well.
The slab side model people are talking about here is the KMK-678GC or "Government Competition" model. This one comes with thumb rest grips and is drilled and tapped for scope rings.