My shrub has two kinds of leaves.  What is this?

The shrub is really just two shrubs that have been pruned to look like one. One is a Euonymus and the other is a Cleyera. You can leave them growing together or remove one of them. If you want to remove one, it would probably be better to remove the euonymus because of the scale problems they have.

Related Videos:
How to Prune Shrubs
Pruning Encroaching or Overhanging Shrubs
Spring Flowering Shrubs

Related Resources:
Shrubs (an index page to many shrub publications by species)
Euonymus
Ternstroemia gymnanthera Cleyera