Plough is the same word as plow, spelled two ways, and the split is purely a matter of national convention: plough has been the accepted spelling in England since about 1700, while American English standardised on plow.
The gh is the interesting part. It records the same throat consonant as in night and daughter, and the Oxford English Dictionary notes that this final rasp began to disappear in the 1300s but was kept longer in the north and in Scotland. So the letters were preserved in the spelling of a sound that had already been dying for four hundred years by the time the spelling was fixed. Plough belongs with the other -ough words — through, though, thought, tough, cough — that are spelled alike and pronounced differently, which is what happens when one spelling has to cover the outcomes of one sound in several dialects at several dates.
plough alternative spelling of plow (Middle English plouʒ, plouh, ploug ). "The accepted spelling in England since 1700" [OED, which also notes that the final guttural began to disappear in 14c. but was retained longer in the north and Scotland]. Related: Ploughed ; ploughing .
plough came in through Old English, and its spelling follows that family's conventions.
What gives it away on the page
| gh | Stands for a throat sound (like the ch in Bach) that English later dropped or turned into f.light, thought, plough, enough |
Old English in the spelling guide · guess another word's family