Refresh method will redraw the whole client area in the map control therefore it's expensive, while Invalidate method is lightweight and will only redraw the area where a change has occurred and a redraw in that area is needed to reflect the changes in the display, i.e., a new feature added to a layer, etc. Therefore, Invalidate method is recommended if map redraw is needed for a portion of the client area. A good example is to draw a feedback geometry on MouseMove event whenever mouse is moved. In such cases Invalidate method is sufficient.

Reference

Map Class
Map Members