Rotating at exactly the same rate as the orbital period around some other body. E.g., the Moon rotates synchronously, relative to the Earth, so that its orbital period and rotational period are exactly the same. As a result, it always keeps one side (the near side) towards the Earth, and the Earth is always in very nearly the same place in the lunar sky (the position depending upon where you are, on the Moon). However, it does still rotate relative to the Sun and stars, at a rate equal to its rotation period, relative to the stars, and equal to its synodic period of rotation, relative to the Sun.

where the orbital period of a satellite is equal to its rotational period, resulting in the same "face" of the satellite pointing towards the planet

A satellite's rotational period is equal to its orbital period; this causes the same side of a satellite to always face the planet. Synchronous rotation occurs when a planet's gravity produces a tidal bulge in its satellite. The gravitational attraction and bulge acts like a torque, which slows down the satellite until it reaches a synchronous rotation.

Phrase describing when a planet's moon takes the same amount of time orbiting the planet as it does spinning. This means the same side always faces the planet.

In astronomy, synchronous rotation is a planetological term describing a body orbiting another, where the orbiting body takes as long to rotate on its axis as it does to make one orbit; and therefore always keeps the same hemisphere pointed at the body it is orbiting.