DICHOTOMY = is a division into two parts, kinds, etc. or even a subdivision into halves or pairs. It is also the division into two mutually exclusive, opposed, or contradictory groups.
Example = This book discusses the dichotomy between Chinese and Japanese cultures.
Dichotomy is when there are two sides to something. i.e. gun rights, abortion rights, etc.
DIVERGENCE = is the act, fact, or amount of diverging, separating or deviating. It is also the total amount of flux escaping an infinitesimal volume at a point in a vector field, as the net flow of air from a given region (this is more a physics/meteorology definition)
Example = Although they researched the project together, their conclusions were a divergence of opinion.
Divergence is when two (or more) things go different ways, the divergence of a friendship, a company diverging because each owner wants to take it in a different directions and thus they split the company.
I hope these definitions and examples give you a better understanding and answer your questions.
~Samantha :)