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Erosion significantly affects the dynamics of gravity-driven mass flows. In snow avalanches, the snow cover can be substantially eroded but only partially entrained, however, there are very limited investigations to substantiate this difference. Here, we study various erosion and entrainment behaviors in snow avalanches using the material point method (MPM), finite strain elastoplasticity and critical state soil mechanics. With varied snow properties, distinct erosion patterns are obtained and analyzed with the mass change rate. When there is significant eroded and entrained mass, properties of released snow and erodible bed snow have clear correlations with the eroded mass, but not with the entrained mass, disclosing the difference in erosion and entrainment. Both enhanced and inhibited avalanche mobilities due to erosion and entrainment are captured under different conditions of snow properties and lengths of release and erodible zones. These new insights may stimulate the development of advanced erosion and entrainment models for large-scale avalanches.