This clarifies the notion of bundle of groups on $X$ with assumption that this is just another name for group bundle on $X$. Following screenshots are from book **A general theory of fiber spaces with structure sheaf by Alexander Grothendieck**. I thought it would be more authentic if I put screenshots than type it. [![enter image description here][1]][1]
[![enter image description here][2]][2][![enter image description here][3]][3]


  [1]: https://i.sstatic.net/kdHGq.png
  [2]: https://i.sstatic.net/65Gei.png
  [3]: https://i.sstatic.net/ev9M3.png