The term irregular moon (or irregular satellite, referring specifically to natural satellites) is generally used to refer to a moon with an atypical orbit, such as Triton with its retrograde orbit, but also referring to other atypical characteristics such as a substantial inclination, e.g., from the ecliptic. For a particular study, a clear definition is undoubtedly stated and observed. Most of the many moons of the outer planets are considered irregular.
It is thought that they are generally captured minor planets.
A regular moon (or regular satellite) is essentially one that is not irregular.