• The effects of Weber number and particle-droplet size ratio are investigated. • For the fixed stationary particle, three regimes are observed: deposition, agglomeration and disintegration. • The deposition regime of the moving particle has two sub-regimes: deposition-I and deposition-II. • For the moving particle, the process of the droplet reaching breakage requires a large initial velocity. • But for the moving particle, the critical initial velocity Vinic depends sensitively on α. Droplet-particle collision is commonly found in nature and industry. The collision of a moving droplet against a fixed stationary particle has been investigated comprehensively, and the collision of a moving droplet against a moving particle also has been studied. However, there is no open literature to conduct a detailed comparison between the two occasions. In this study, the collision of a droplet against a moving/fixed stationary particle are studied by the lattice Boltzmann method, and a comprehensive comparison is made. The effects of Weber number and particle-droplet size ratio are investigated. For the collision of a moving droplet against a fixed stationary particle, three regimes are observed: deposition, agglomeration and disintegration. For the collision of a moving droplet against a moving particle, only two regimes are observed: deposition and disintegration. Moreover, for the first time, it is observed that the deposition regime of a droplet colliding against a moving particle can be divided into two sub-regimes. The variation of force of the particle is analyzed. The numerical results show that the amplitude of the vertical force of the fixed stationary particle is larger than its moving counterpart, although the fluctuation of the former will disappear quickly. The present study reveals the differences between the two collision situations, which are helpful to understand the collision phenomena in industrial applications.