* Sidereal Month: This is the time it takes the Moon to complete one orbit around the Earth relative to the stars. It's about 27.3 days.
* Synodic Month: This is the time it takes the Moon to complete one cycle of phases (from New Moon to New Moon). It's about 29.5 days and is the basis for our calendar months.
The difference between these two types of months is due to the Earth's own movement around the Sun. As the Earth orbits the Sun, the Moon needs to travel a little further than a complete orbit to catch up to the same position relative to the Sun, hence the longer synodic month.
So, the length of a month in astronomical terms depends on what you're measuring.
