Can anyone explain the main differences between the three types? Not how they look but how they fly and why a certain type is preferred over the other.

I see most profiles are modeled after scale aircraft and most full-scale aerobatics are done with Extras/Edges/SU-29s/Yaks, etc. What sets those designs apart from a pattern aircraft and why are there no full-scale pattern aircraft?

Thanks, just trying to figure all this stuff out

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)).

Here's my take on the flying aspect.

Models that represent full size planes in true scale usually have undersized control surfaces, and require extra nose weight to balance correctly. For those reasons, flight characteristics are usually not agile / aerobatic and landing speeds tend to be fast.

Profile planes are inherently lightweight. Designers tend to make them overpowered with abundant control surface area, for agility and perhaps hovering capability. They usually land at walking speed.

Pattern is a whole different subject. Designers want agility during maneuvers, and stability during straight line flying. That makes for nice flying planes, usually expensive.

Many designs emulate full scale planes, with increased control surface area and light structures, for easy flying and slow landing speeds. Those don't fall precisely into the scale or pattern categories.

Just my 2ΒΆ worth, let's see what others have to say.
Dave Olson