  We use PHANGS-JWST data to identify and classify 1271 compact 21 $\mu$m
sources in four nearby galaxies using MIRI F2100W data. We identify sources
using a dendrogram-based algorithm, and we measure the background-subtracted
flux densities for JWST bands from 2 $\mu$m to 21 $\mu$m. Using the SED in JWST
as well as HST bands, plus ALMA and MUSE/VLT observations, we classify the
sources by eye. Then we use this classification to define regions in
color-color space, and so establish a quantitative framework for classifying
sources. We identify 1085 sources as belonging to the ISM of the target
galaxies with the remainder being dusty stars or background galaxies. These 21
$\mu$m sources are strongly spatially associated with HII regions ($>92\%$ of
sources), while 74$\%$ of sources are coincident with a stellar association
defined in the HST data. Using SED fitting, we find that the stellar masses of
the 21 $\mu$m sources span a range of 10$^{2}$ to 10$^{4}~M_\odot$ with
mass-weighted ages down to 2 Myr. There is a tight correlation between
attenuation-corrected H$\alpha$ and 21 $\mu$m luminosity for
$L_{\nu,\mathrm{F2100W}}>10^{19}~\mathrm{W~Hz}^{-1}$. Young embedded source
candidates selected at 21 $\mu$m are found below this threshold and have
$M_\star < 10^{3}~M_\odot$.
