There are substantial differences and similarities between routers and shapers. The similarities are with function and the differences are in performance. Both tools are stationary and the operator moves the work, not the tool. Both use fences, collars or bearings to control the path of the work.
Shapers are essentially for edge or end cuttings.
They are cabinet shop and millwork tools, and as such are heavy handed, heavy duty and heavy weight. They are designed for all-day door, drawer or molding operations. They are production animals. Although capable of experimental work, shapers are usually set up for routine big jobs of long duration. Router tables are welter weights by comparison.