I was born in Jan "44, and Dad bought his first combine, an AC model 60, and a Roto Baler, in 48 and 49....I"m thinking the combine came first, cuz Dad was supposed to get the first baler shipped in, but the neighbor"s son worked at the dealer, and when the baler came in, he told HIS dad that his baler had arrived so he got it. Bottom line, I do remember seeing a straw pile in the cow yard, like Dick 2 describes, so I was about 3yo then.
Regarding your pic, I see that the machine has an elevator for clean grain, maybe a paddle elevator, since it"s round? Some threshers had a grain tally, a trip mechanism, that measured and counted bushels going into the wagon. Sort of like today"s dump weigher.
Yes, the correct spelling is thresher. My uncles, with a German (Cherman) accent, just called them trash machines, but meant threshing. The word trash did not describe the output!