When using Auto Move With Gaps, all succeeding Sequenced Tasks will be moved.
The best way to further explain this is through a simple example. Imagine the following Schedule where the first Task is to be dragged from the 14th to the 15th (see highlighted below).
So the Task on the 14th will be moved to the 15th, the Task on the 17th to the 18th etc - see below. The Gaps between the Tasks will be retained.