Using hyper-parallel tempering Monte Carlo simulation, multiple histogram reweighting method, and finite size scaling, we investigate the adsorption of fully flexible and rod-coil chains on the square lattice. We find that the phase behaviour changes with the chain length and flexibility. For homonuclear rod-coil chains, the phase diagram consists of only gas-disorder liquid critical point. Weakening of the interaction energy between the segments belonging to two different subunits gives rise to an order-disorder transition. The topology of the resulting phase diagram depends on the chain length and flexibility. For short chains, both fully flexible and rod-coil diblock copolymers form lamellar ordered phase with fully stretched chains, and the order-disorder transition is of the first order. The phase diagrams are similar for both chain architectures and consist of two binodals meeting in the triple point. When the chain length increases the order-disorder transition becomes second-order and the difference in the phase behaviour between the fully flexible and the rod-coil diblock copolymers becomes more pronounced. While for the former chain architecture the topology of the phase diagram involves a λ-line which meets the gas-disordered liquid binodal in the critical end-point, in the latter case the λ-line meets the gas-disordered liquid critical point and forms the tricritical point. We trace back these changes to the change in the morphology of the ordered phase. The mechanism of the order-disorder transition involves the formation of domains resembling those observed during the spinodal decomposition process. The domains subsequently merge and arrange into lamellae. These observations are supported by integral geometry analysis.