DeSelle:
The gray painted parts are for what is known as a "pump jack engine". These were self contained units consisting of a small hit-and-miss engine, gearing, crank and motion to work a pump on a domestic water well (such as a country home or farm might have). Not sure, but the pump jack engine may be a Fairbanks-Morse unit.
The green painted casting which is partially shown to the right of your photo is for another engine altogether. That green casting from what I can see, consists of the cylinder, cooling hopper (a reservoir for cooling water, usually cast integral with the cylinder), cylinder head, and magneto mounting bracket.
There are a lot more parts required to make either of these engines operational. Often, the crankshaft and flywheels are removed from the horizontal engines of this type to make moving them easier. The horizontal engine is missing its exhaust valve rocker arm, rocker arm pin, push rod and latch (for the hit and miss governing). The hit and miss governing would hold the exhaust valve open when the engine reached governed speed. As the speed dropped off, whether due to load, or simply coasting down, the hit and miss mechanism would allow the exhaust valve to work normally. This caused the engine to fire or "hit". The result was hit and miss governed engines never did run at a steady speed.
If the green engine is a Fairbanks-Morse model Z, it is likely a throttle governed engine and a lot simpler mechanism.
Engines of the types you have shown usually had what was known as an "automatic" or "atmospheric" intake valve. The intake valve had a light valve spring and opened when the downstroke of the piston created a partial vacuum in the cylinder. No cam and tappet or pushrod/rocker was used.
As they say, "the devil is in the details". While the major castings for two different engines are shown in your photo, there are a lot of other parts needed to make either engine operational. The green engine will need a set of timing gears to drive the exhaust valve cam and the magneto. It will also need its governor, crankshaft, flywheels, main bearing caps, magneto and "mixer" (an old time term for a carburetor). The fuel tanks for these engines were made of light gauge tin-plated steel, soft soldered together. On the green engine, the fuel tank was likely in the hollow base casting. These tanks tended to rust out or be dented and damaged, so are usually not found with an old engine in the condition you show in your photo.
The green engine was likely built as a "power unit", meant to be belted up to anything the user needed to run. It is probably a bit light for running a buzz saw, but would be belted up to run something like a vacuum pump for milking machines, woodworking machinery, a small grist mill, or similar. The gray engine, being a pump jack engine, was built integral with the mechanism to work a water pump on top of a water well. In your photo, to the LH side of the engine, above the spark plug, there is a knob with a spring on the valve stem. This is part of the "mixer" (carburetor). In the foreground there is a bull gear with a crank pin. This crankpin received a connecting rod which worked a yoke attached to the piston rod of the well pump. The well pump usually consisted of a pump head, with the discharge of the pump. A sectioned rod ran thru this pump head, and down inside a steel discharge pipe to the bottom of the well. The discharge pipe was connected to the actual pump cylinder (made of brass or bronze). The piston in this pump cylinder was packed with leather cups, and there was a suction valve on the pump cylinder. What you have is most of the pump jack and engine.
Provision was usually made on the pump head so that water could be pumped up manually if the engine failed to start. During the Great Depression, my father was an Ag student at Cornell University. Summers, he had to co-op on a farm that the school assigned him to. For the farmer, it was free labor, as the Ag students worked for their board. Dad kept notes as was required by his professors. In dad's notes, he describes a typical morning in 1935 on a sharecropper's farm in the Finger Lakes region of NYS. Days began at about 4 AM. Dad's notes tell of a drought and all the water wells on the farm where he was working as having dried up. Dad would get up at about 4 AM or 4:30 AM, curry and harness a team of draft horses and hitch them to a tank wagon. He would drive the team and wagon to a neighbor's farm. The neighbor had a hit and miss engine driving a pump jack on a water well that had not run dry. Dad's notes describe how he was taught to start the hit-and-miss engine, using his fingers as the choke, and how many turns to open the mixer valve when starting, then cutting it back once the engine caught and ran. Dad's notes describe some mornings when he could not get the hit and miss engine to start, so he pumped approximately 250 gallons of water into the tank wagon by hand. He then drove the team back to the farm, unhitched the team, and he and the farmer would fill the livestock water troughs and bring buckets of water into the farmhouse.
People who wax nostalgic for "the good old days" never had a morning or two like my father had, dealing with a cantankerous hit and miss engine and having to pump water by hand. Your pump jack engine may well have been used in conjunction with a windmill (Aeromotor offered air cooled pump jack engines, F-M offered water cooled pump jack engines). The idea was that the windmill was the primary means of driving the pump. If things were dead calm, or water was wanted in a hurry, the pump jack engine would be started. As a last resot, the handle could be pinned onto the pump and water pumped up by hand.
There are plenty of sources of parts for these old hit and miss engines, including new gaskets, period-correct ignition wire, large-thread spark plugs, and much else including some decals. Neighbors and friends have a few hit and miss engines, and I've made some parts for them. The collecting and showing of these old hit and miss engines has become more popular, and prices for the engines has risen sharply. Up in our Catskill region, there are some very fine trout streams. Along one such stream, the land is held by a few very wealthy old families. A man who restores and builds reproductions (full sized) of the hit and miss engines at 40 grand a copy, has a ready market with the wealthy men who have country homes along that trout stream. These guys who never did a day of manual labor for pay in their lives discovered hit and miss engines and have them as showpieces or playthings. Between guys like them and the steam punk crowd snatching up lubricators and petcocks for their kitsch, the hit and miss or other old engine hobbies have become a good bit more expensive, so be forewarned.