The nature of the globule-coil transition of surface-confined polymers has been an issue of debate. Here this 2D collapse transition is studied through a partially directed lattice model. In the general case of polymers with positive bending stiffness (Delta>0), the collapse transition is first order; it becomes second order only in the limiting case of zero bending stiffness (Delta triple bond 0). These analytical results are confirmed by Monte Carlo simulations. We also suggest some possible future experiments.