Generalized parameterization of the differential thick-target neutron yield (TTNY) is obtained by studying systematics in the differential TTNY based on moving source parameters deduced from experimentally obtained differential TTNYs for light and heavy ions. The yields of equilibrium neutrons (ENs) and nonequilibrium neutrons (NENs) are expressed by simplified expressions. The variation of the nuclear temperature of the EN is scaled with the excitation energy transferred to the target-like fragment. The nuclear temperature of the NEN is reproduced fairly well by the Fermi gas model. The scaling of the velocity parameter of the EN is considered based on the breakup fusion mechanism. The velocity of the NEN component is compared with the corresponding data for the proton emission. The velocity is related to the relative speed between projectile and target nuclei at contact.