I don’t really understand how the combustion could be anywhere but internal, so why do they bother specifying it?
Stirling cycle engines are external combustion.
Sure, there are external-combustion engines - any steam engine, for instance, or Stirling-cycle engines. The difference is that the working medium (the liquid or gas that pushed on a piston or turbine or something mechanical) in an EC engine isn’t directly produced by combustion and then dumped overboard; instead it’s heated externally. The advantage of such a system is that you can use almost anything for fuel and can optimize your combustion system for thermal efficiency and emissions.
You can find some more Stirling Cycle links here.
Whoa, hey, kewl stuff! 
How it works (the short version).
http://www.sfu.ca/~sfungc/stirlingengine.htm
How it works (the Big Brain version).
http://electron6.phys.utk.edu/phys136/modules/m3/m3ex1.htm
Build a Tin Can Stirling Engine in your basement!
http://comptune.com/tincan.htm
So, tell me again why I don’t have one of these marvelous engines as the pusher in my soccer mom Caravan?
The swashplate mechanism has a lot of problems to face with friction losses and basic reliability. Also, the high lateral loads placed on the pistons affects the sealing and life of the rings. The operating medium has to be kept well sealed from the outside, limiting your ability to provide lubrication where you need it most - your car engine can run fine a quart low, but not a Stirling.
The theoretical thermodynamic efficiency of the cycle, and the ability to use anything as a fuel, are attractive, but people have been working on the concept for a century or so without adequately fixing the practical problems.
There’s a lot of talk and rumour around right now about Dean Kamen and his new “Ginger” invention which, as nearly as anyone seems to be able to determine, is a Sterling-powered urban commuting scooter. See http://GINGER.patentcafe.com/ for details… such as they are 