lateral and parallel thinking   (link)

http://www.edwdebono.com/debono/lateral.htm
lateral thinking is what the buzzphrase "thinking outside the box" refers to. it usually involves rejecting one or more of the assumed constraints or assumptions and attacking a problem in a new way.
lateral thinking puzzles

parallel thinking:
With the traditional argument or adversarial thinking each side takes a different position and then seeks to attack the other side. Each side seeks to prove that the other side is wrong. This is the type of thinking established by the Greek Gang of Three (Socrates, Plato and Aristotle) two thousand four hundred years ago.

Adversarial thinking completely lacks a constructive, creative or design element. It was intended only to discover the 'truth' not to build anything.

With 'parallel thinking' both sides (or all parties0 are thinking in parallel in the same direction. There is co-operative and co-ordinated thinking. The direction itself can be changed in order to give a full scan of the situation. But at every moment each thinker is thinking in parallel with all the other thinkers. There does not have to be agreement. Statements or thoughts which are indeed contradictory are not argued out but laid down in parallel.In the final stage the way forward is 'designed' from the parallel thought that have been laid out.