I have wondered the same thing.
I'm left handed, but play right handed. When I first picked up a guitar, I didn't even know there was such a critter as a left-handed guitar. To be fully up front, I'm not sure how left-handed I am. I write left-handed, eat left-handed and play pool left-handed. I can (or have learned) to use hand tools both ways, but if I pick up a screwdriver, it's with my left hand. I throw a ball right-handed and I kick right-footed. When I played baseball as a kid, I batted right-handed.
Before I retired, my business partner was also a lefty. He wanted to learn guitar, so I loaned him one of my guitars. He made no progress on it for several months. One day he decided to go to a local music store and pulled a left handed Strat off the wall. He was immediately more comfortable with it and ended up buying one. He never really followed it up and the Strat is more of an art piece in his house now.
When I did the setup on his lefty Strat, it seemed entirely foreign to me. Just tuning it was extremely awkward for me and getting my brain around the entire setup process took me at least twice as long as if I was working on a righty instrument.
Steve Morse, who won the Guitar Player Magazine guitarist of the year reader's poll for five consecutive years is left-handed, but plays right. On the other hand (yes, I said it), Eric Gales is right-handed but plays guitar left-handed. He adds a bit extra in the fact that with the left hand orientation (pick left, fret right), the guitar is still strung as if it was played right handed.
Probably doesn't help you much, but I'm convinced there are degrees of left-handed-ness.