In glassy materials, the Johari-Goldstein secondary (β) relaxation is crucial to many properties as it is directly related to local atomic motions. However, a long-standing puzzle remains elusive: why some glasses exhibit β relaxations as pronounced peaks while others present as unobvious excess wings? Using microsecond atomistic simulation of two model metallic glasses (MGs), we demonstrate that such a difference is associated with the number of string-like collective atomic jumps. Relative to that of excess wings, we find that MGs having pronounced β relaxations contain larger numbers of such jumps. Structurally, they are promoted by the higher tendency of cage-breaking events of their neighbors. Our results provide atomistic insights for different signatures of the β relaxation that could be helpful for understanding the low-temperature dynamics and properties of MGs.