how come not every atom in the CONECT section is described in the SITE section?
Because it is not required and not needed.
CONECT is for listing bonds, so that molecular graphics programs know how to draw the structure.
SITE is for annotation of interesting sites. Each listed SITE has a corresponding REMARK 800 that "details its significance". A graphical program may provide a menu with a list of all interesting sites for easy navigation.
Note: PDB is a legacy file format. The primary file format used nowadays by the PDB (organization) is called PDBx/mmCIF. So when looking into such details it is often better to look directly into mmCIF files.