The cipher's arithmetic — subtracting the plaintext from the key instead of adding — appears in Giovanni Sestri's 1710 treatise, almost a hundred and fifty years before the name everyone uses. Like so many ciphers, it was reinvented independently and the most famous name won.
Sir Francis Beaufort (1774–1857) was a Royal Navy hydrographer, the officer who gave the world the Beaufort scale of wind force — the "force 8 gale" scale still used in shipping forecasts. The cipher published under his name (posthumously, in 1857, by his brother) was something he apparently used privately for family correspondence. There is no evidence he claimed originality; the cipher itself was likely picked up from published sources of his time.
The variant Beaufort (cipher = plaintext − key) has an even more distinguished career: it is essentially the arithmetic the German army's M-209 converter of the 1930s–1940s used inside its more elaborate mechanical construction. A discarded variant of one century became a component of a field machine in the next.
For a working cryptographer of the 1800s the three siblings — Vigenère, Beaufort, variant Beaufort — were one tool with three settings. Manual encyclopedias listed them together, and the choice between them was a matter of taste: only classic Beaufort's self-reciprocity (one table lookup serves both encryption and decryption in the field) was a practical argument. Against a determined cryptanalyst all three fell together, once Kasiski published the periodicity attack in 1863.