They look similar, but as to commonality, I doubt that there is much you could easily swap out between them. The Tempest used a completely new, thinnner, wing. The front fuselage was lengthened to accomodate an extra fuel tank (to cover for the loss of fuel storage in the wings) and because of this a new tail (with more surface area) was needed too. They use similar construction techniques, with a steel tube fuselage cockpit section mated to a semi-monocoque rear fuselage and tail.
Edit: just to illustrate the development path a bit more, this is the Hawker Tornado, an early parallel development version of the Typhoon. This airframe was built up from two airframes that were in production when the order for Tornados was cancelled. It was re-engined with a Centaurus CE.4S engine and used as a testbed for various Centaurii, leading to the later Tempest II.
15_002600 Hawker Tornado HG641 by
SDASM Archives, on Flickr