Both are “collapsed”. A is collapsed in position, B is collapsed in momentum. Of course, this requires A to be “un-collapsed” in momentum, and B to be “un-collapsed” in position.
It would be much more clear if instead of saying “collapsed” we said: the object’s wave function has collapsed (changed) so that it is only composed out of a single plain wave, guaranteeing you can only get one possible result should you measure the associated variable, on the associated particle; and consequently the wave function in the conjugate basis will be a combination of every possible plain wave in that basis (typically an infinite number of them), leading to you getting a random result should you try to make a measurement associated with that basis. But instead people get lazy and say collapsed, leading to people who only read the headlines thinking a particle can collapse; or worse that there is something magical about this.