Pedantically shorting doesn’t have to be borrowing the underlying instrument. Put options are another way to trade on the idea that a stock will go down. I’d actually bet it’s the more common way. It would still be colloquially referred to as being short.

That's actually the opposite of "pedantically" given that you're playing loose with the definition. Pedantically, shorting is selling a financial instrument you don't own, with the idea (though it is not a requirement to fit the definition) that you'll give it back later by buying at a price lower than it is now.

What you described is options trading, one method of which hedges against declines in stock price. Yeah, one could take a "short" position by buying puts, but it can be argued that a short position is not what puts were originally designed for. In contrast to short sellers who obviously intend for the price to go down, or they won't make any money.

I do question whether puts are the "more common way" given that they have an expiration. You can hold on to a short sell as long as you can pay the interest and the loaning party doesn't want their shares back.

Arguing over the definition of Pedantic. I think we've reached peak HN.

"Short selling" refers to selling borrowed shares. "Being short" is the opposite of "being long" and refers to exposure, irrespective of the instruments or methods used to attain it. TL; DR one can be short through options or short selling.

Pedantically, I would agree with your definition if it was phrased as "short selling" and would ask for more clarification ("via what?") if someone said they had a short position.