[Edited] Confused with the relationships between vertex groups, weights, and bones

After struggling with google and rewatching the courses, I am still confused with the relationships between vertex group and bones. As I am concerned, a sing vertex is influenced by different vertex groups according to weight, but it seems that the deform of a single vertex group can be influenced by different bones (also can be influenced by a single bone as showed in the eye lesson). I just wonder how bones affect the vertex group? And where shows the relationship between them in blender? Thanks!