Slitherine

Am not sure if I asked this before or if there was a reply, but:

What is the difference on the CMT between:

a) Turn or wheel to face enemy within 2MU (Simple/Simple)

and

b) A change of formation or facing while otherwise stationary (>2MU Simple/Complex)(<=2MU Complex/N/A)

Can I turn a unit to face 90 degrees left or right as a simple move as long as I move some actual distance then? (How much is necessary?)

The first is a move to line up facing an enemy in close range.

The second (for which you need a CMT at close range) is to change formation, or facing if for some reason you want to do something other than turn to line up.

The formation change is sometimes used to snap into an extended line (to double firepower), or to change between skirmish and tactical formation.
If Cavalry race up to 2MU of you, a CMT into square will save the automatic drop when they charge you next turn.

a) Turn or wheel to face enemy within 2MU (Simple/Simple)

and

b) A change of formation or facing while otherwise stationary (>2MU Simple/Complex)(<=2MU Complex/N/A)

As Brett says, (a) is used to line up facing an enemy within 2 MU. However, this may well expose your unit to a flank charge (as an example), so you may not want to exactly face the enemy within 2MU, therefore with a CMT you can partially face it while not leaving your flank exposed. and of course, you just may want to change formation (square to tactical, tactical to square, tatical to line etc.).