The adjective sidereal means based on the celestial sphere, the "fixed" position of the stars (presumably galaxies and distant stars).
A sidereal period is the orbital period of a body, counting as one orbit, one cycle around the "host" body, back to the same sky position as seen from the orbited body. For example, we may think of the Moon as having completed an orbit when it is back over our head at a certain time of day (e.g., the midnight when the Moon is nearest the zenith). However, the Earth orbits a bit each day and that given time of day occurs with the Earth facing a different direction relative to the distant stars. So that concept of the Moon's orbital period does not match its sidereal period.
Sidereal time is time based upon the position of the stars, e.g., without respect to the position of the Sun and moon as we see it, or other adjustments. A sidereal year is the Earth's sidereal period (365.2422 days), a sidereal month is the Moon's (27.32166 days), and a sidereal day is the time it takes the Earth to turn until the same stars are overhead (roughly 23 hours 56 minutes 4 seconds).