How does an ETOPS APU start in-flight?
Some aircraft may have a special "ETOPS APU" that can be purchased, but many aircraft simply have THE APU that they come with. It is maintained to the standards required in the approved ETOPS program, and is either run during the ETOPS portion of the flight, or else has some means to ensure that it will reliably start even when cold-soaked. (For instance, at least one ETOPS program requires that the APU be started shortly before the top-of-descent on enough flights to "prove" that it does, in fact, start up reliably even in a worst-case cold-soaked scenario.)

Most (perhaps all) APU's in aircraft currently in production have the general capability of being started in flight, so that particular aspect of things isn't unique to the ETOPS world.  Documenting the reliability of the APU is a uniquely ETOPS thing, but so much of ETOPS is about exactly that: demonstrating and documenting just how reliable the hardware is. 

It often isn't different hardware, but the same equipment as in a non-ETOPS aircraft, but maintained &amp; tracked to higher standards.