Classical Cepheid stars are supergiants of greater than 2-3 solar masses, that at the end of main-sequence H burning move across the HR diagram to become red giants, crossing the Cepheid instability strip.
The type-II Cepheids are low-mass, high-luminosity pulsators, with periods from 1-40 days. These evolved stars have a He core surrounded by an outer H shell. The type-II's are sub-divided into the BLHer, WVir, and RVTau sub-types.
Dwarf Cepheids are short period pulsators that are found where the Cepheid instability strip crosses the main sequence. The delSct sub-type of dwarf cepheids have periods of 30-min - 8-hours, spectral types A-F, and have photometric amplitude variations of > 0.3 magnitude.
RRLyr stars are short period (< 1 day) pulsators, horizontal branch stars that are in the Cepheid instability strip. The RRLyr stars are older, less-luminous stars than the classical Cepheids.
Cepheid stars are common, click here for a short catalog of representative Cepheid stars.