Reading this thread which talks about V4 motors, I am wondering what exactly is the difference between a 180° V4 motor you'd find in a Subaru and a true boxer (or horizontally opposed) flat 4 cylinder?
tl;dr: In common usage, there isn't a difference. The Subaru flat-4 is a boxer.
Here's a lovely picture that I found on the Manchester Subaru site (I'm not a customer but I'm always encouraged when a dealer is willing to provide useful technical material!):
As you can see from that picture, the pistons are moving in pairs: the two in the rear are in and the two in the front are out. This is where the boxer gets its name: the pistons look like they're punching each other.
Getting into the technical details (see the great Wikipedia entry on flat engines):
True boxers have each crankpin controlling only one piston/cylinder while the 180° engines, which superficially appear very similar, share crankpins. The 180° engine, which may be thought of as a type of V engine, is quite uncommon as it has all of the disadvantages of a flat engine, and few of the advantages.
You have to look closely at the image above but you can see that the pistons are not sharing crank pins. In the image below we can see a true 180 degree V6 (on the left with shared crank pins) compared to a boxer flat-6 (on the right with individual crank pins as in the Subaru).
As stated in the article, however, the 180 degree V4 is quite uncommon due to its technical limitations. Note those arrows in the left-hand diagram: instead of having opposing pistons box each other (somewhat cancelling vibration), they would be reinforcing each other. This would cause a truly distressing torque of the whole engine around the vertical axis, with the direction changing every half rotation of the crankshaft.
As the 180 degree V4 with shared crank pins is so uncommon, the flat-4 boxer effectively takes its place in terms of "what would you do if you need to increase the angle to 180 degrees?" Therefore, in the common usage we consider a 180 degree V4 and a flat-4 to be effectively the same thing.
I would like to add that only TWO companies in the world manufacture boxer engines: Subaru and a German brand. The reason is that they are complex to manufacture. Also, Subaru uses a chain to time their overhead valves, most companies prefer belts to time.
The two most common types of piston arrangement are vee configuration and inline configuration. Vee is the very best, IMO.
The difference in a 180° crank and a "normal" engine crankshaft (cross-plane) is the position of the rod journals.
On a cross-plane crank, the crank pins are 90° from each other but in a 180°, or flat plane crank, the pins are 180° from each other. In other words, on a flat-plane crank, the rod journals are all on the same plane, so the crank looks like it is for an inline engine. Ferrari, Lambo and most exotics use a flat plane crank while most American V#s use a cross-plane crank.
A standard 4 cylinder crank is a simple example of a flat-plane crank. Both the Subaru and VW Beetle air cooled are flat-planes, or 180° cranks, and are "boxers".
Yamaha went to a cross-plane in their R1 4 cylinder to smooth the engine.
So, basically, any crank with the rod journals at 180° is a flat-plane, or 180° crank, whether it is a "boxer" or not.