The Difference Between Component Analysis and Factor Analysis

The common factor model assumes that there is a dimension, or multiple dimensions, that influence a set of variables. A component model instead, creates out of the variables a composite. If you have ten items, you can get up to ten composites. But why on earth would you do that? Because all you've done is traded ten items for 10 composites. So then the fun becomes, can we take that ten dimensional matrix and reduce it to a smaller number of composites that is good enough for government work.