I had a friend ask me today if “to the right” is the same as “on the right,” which was what she had previously learned. I really couldn’t give her a definitive answer. One could say a particular person’s politics is to the left/right of,say, Rush Limbaugh, not on the left/right of. I can’t say if, when giving directions, “the drugstore is on the left” or “the drugstore is to the left” is more correct or if there’s a difference. Is it an American/British thing?
I would say that “to the right” is more general. Like, somewhere over there.
“On the right” is more like a definitive spot on the right.
But I don’t think it actually matters in direction and location context.
depends on the circumstance a bti i guess but generally i think of it like this: IT’S on the right and GO to the right. obviously not necessarily those 2 exact words but the meaning behind them. Could be the TB talking, but its how it seems logical at this second.
Doh. Isn’t it obvious that ‘to’ is indicative, while ‘on’ is positional. 
Like Pingdong said: like ‘go’ and ‘at’.
Thanks. I feel much better now that I have an answer backed up by an authoritative “duh.” 
So it’s a common misuse, like “for all intensive purposes” instead of “for all intents and purposes” and not an American English / British English problem.
I think we should teach the phrase “on your left” now that everyone rides a bike in the city.
To the left, to the left,
Everything you own in the box to your left…