Scale:
Any model that reproduces a full scale airplane.
There are more or less strict competitions regarding details and proportions.
They tend to be heavy models, and not very aerobatic.

Profile:
Any model which fuselage is not build-up or it is represented only in two dimensions.
They are simpler to build, but all the guts stay outside.
Any type of model can have a profile fuse, even some forms of scale (Navy carrier control line).

Pattern:
Any non-scale model that is specifically designed to comply with a sequence or pattern of aerobatic maneuvers.
They don't look like real airplanes because they fly in different conditions (air reacts differently for little and big airplanes (read about Reynolds number)).