A synodic cycle begins with a conjunction of two bodies and ends with their next conjunction, after one of them has completed an orbit and then caught up with the slower body.
If the name of the cycle contains two planets, for example Jupiter-Saturn synodic cycle, it refers to the conjunctions of those two planets.
If the name only contains one planet, for example Jupiter synodic cycle, it refers to Jupiter conjunct the Earth from a heliocentric perspective. From a geocentric perspective that would be the Sun-Jupiter opposition, when Jupiter is retrograde. In case of the inner planets, the cycle begins with the inferior conjunction, when the planet is retrograde and between the Earth and the Sun.
The period between two New Moons is called a synodic month. It is 29.53 days long on average.