We compare a lattice-based computational model to an off-lattice individual-based approach for growing cell populations. After summarizing the fundamental properties of the existing off-lattice model, we present its on-lattice approximation and a possible way of their simulation. By performing in silico experiments, including single-cell and multicellular simulations, we show that the collective behavior of the agents is similar in both models, even though there are differences in the individual-level attributes.