If you are buying "put options" = puts, how is that really shorting when you are not borrowing shares for that, and shorting (excluding naked shorting) is either possessing, or borrowing shares, selling them for a later cover at a lower price, unless this is a method I am not familiar with?
If you are dealing in puts vs shorting then there would be a difference, but then they are not the same thing imo, any more than buying calls and going long is the same.
When you said you were actually shorting sounds like you meant you were just buying options and meant shorting in a veryyyy general sense.