Both types of lens enable us to change focal length and focus distance.
Zoom lenses keep the focus when we change the focal length. Vario lenses generally don’t.
The change of focal length is usually achieved by changing the relative position of lens packages. During this process, the principal planes move.
For zoom lenses this adjustment is done with the very same Ringthat is used for the change of focal length. Vario lenses use a different adjustment ring for this.
see also: How to tell which sensor size a zoom lens was designed for?
see also: I can’t focus my lens to infinity#This lens doesn’t focus, but another zoom lens does