Really clear explanation here, in the context of considering your own essay writing.
Missing is the fact that sentences can be compound and complex at the same time, or multiply compound and complex -- with many clauses coordinated or subordinated. It also disregards the 'minor sentence' -- that is, a word, phrase or fragment on its own, marked out as a sentence but with less than a full clause.
http://www2.ivcc.edu/rambo/eng1001/sentences.htm
