On business was originally on BA metal only but has expanded to include a few joint business partners e.g. AA. As layz indicates you only get On Business points on non BA metal if you book the BA codeshare flight number. The amount of On Business points you get is also small e.g. 200 points for an AA operated flight booked under a BA codeshare.
The BA codeshare requirement is often a big restriction e.g. you can get On Business points on some Qantas domestic flights in Aus but say you want to fly from Syd to Perth where there are lots of Qantas flights daily but only one of them has a BA codeshare number attached to it.