Period-colour and amplitude-colour (PCAC) relations can be used to probe
both the hydrodynamics of outer envelope structure and evolutionary
status of Cepheids and RR Lyraes. In this work, we incorporate the PCAC
relations for RR Lyraes, BL Her, W Vir, and classical Cepheids in a
single unifying theory that involves the interaction of the hydrogen
ionization front (HIF) and stellar photosphere and the theory of stellar
evolution. PC relations for RR Lyraes and classical Cepheids using the
Optical Gravitational Lensing Experiment (OGLE-IV) data are found to be
consistent with this theory: RR Lyraes have shallow/sloped relations at
minimum/maximum light, whilst long-period (P > 10 d) Cepheids exhibit
sloped/flat PC relations at minimum/maximum light. The differences in
the PC relations for Cepheids and RR Lyraes can be explained based on
the relative location of the HIF and stellar photosphere which changes
depending on their position on the Hertzsprung-Russell diagram. We also
extend our analysis of PCAC relations for type II Cepheids in the
Galactic bulge, Large and Small Magellanic Clouds using OGLE-IV data. We
find that BL Her stars have sloped PC relations at maximum and minimum
light similar to short-period (P <10 d) classical Cepheids. W Vir
stars exhibit sloped/flat PC relation at minimum/maximum light similar
to long-period classical Cepheids. We also compute state-of-the-art 1D
radiation hydrodynamic models of RR Lyraes, BL Her and classical
Cepheids using the radial stellar pulsation code in MESA to further test
these ideas theoretically and find that the models are generally
consistent with this picture. We are thus able to explain PC relations
at maximum and minimum light across a broad spectrum of variable star
types.