The terms forge and furnace appear to have been used interchangeably to some extent in Colonial times.
A typical furnace would be twenty feet or more in height, about twenty-four feet across the base, and sixteen feet at the top, tapering upward like a cone or pyramid with the top sliced off. It's function was the reduction of ores to crude pig iron through intense heat. The iron was run off to harden in sand molds.
The smelting process was accomplished by charging the furnace from the top with alternate layers of ore, charcoal, and oyster shells or limestone. The lime combined with ore impurities to make a slag which floated on the top of the refined iron. The iron was tapped off at the bottom and the slag drawn off higher up the side of the furnace every ten hours.
Charcoal was the ideal fuel in the days before anthracite coal came into use and provided superior. Hickory made the best charcoal but apparently any wood at hand was used on occasion. The average furnace used the wood from about 240 acres of land each year.
A forge was a more refined version of the furnace. Pig iron from a furnace, often on the same site, was resmelted and refined into malleable bar iron.
Pig iron could be cast into pots, pans, kettles, firebacks, stoves, and sash weights. But "bar iron" or wrought iron was required for products which had to be pounded into shape and required great strength. Thus tools, wheel rims, and horse shoes were made from this material.
As iron was resmelted in the forge fire, it was beaten with heavy hammers, often weighing five hundred pounds. These were raised by a water wheel and then allowed to fall upon the molten metal. This process removed impurities.
Also found in early iron works were rolling mills, where heavy rollers flattened wrought metal into sheet iron, and slitting mills, which employed mechanical shears to turn out iron rods from which were made nails, wagon tires, and other similar products.