  We show that the X-ray and $\gamma$-ray spectra of Swift GRBs and their
afterglows are consistent with the emission characteristic of an expanding,
relativistic fireball. The classical afterglow due to the impact of the
fireball on the external medium is often not observed until one to several
hours after the GRB. Focusing on GRBs 061121, 060614, and 060124, but
generalizing to the full ($>$50 Msec XRT exposure) Swift sample up to and
including GRB061210, we show that the early emission in $>$90% of early
afterglows has a characteristic $\nu F_{\nu}$ spectral energy $E_{\rm peak}$
which likely evolves from the $\gamma$-rays through the soft X-ray band on
timescales of $10^2-10^4$s after the GRB. The observed spectra are strongly
curved when plotted with logarithmic axes and have often been incorrectly
fitted in other studies with a time-varying soft X-ray absorption. The spectral
evolution inferred from fitting instead models used to fit GRBs demonstrates a
common evolution--a powerlaw hardness intensity correlation and hard to soft
evolution--for GRBs and the early X-ray afterglows and X-ray flares. Combined
with studies of short timescale variability, our findings indicate a central
engine active for longer than previously suspected. The GRB spectra are
observed to become very soft at late times due to an intrinsic spectral
evolution and due to the surprising faintness of some afterglows. We discuss
models for the early X-ray emission.
