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The term habitable zone (HZ) has generally been used for the region of space where a planet can hold liquid water (i.e., surface water), which is considered a prerequisite for life as we know it. More specifically, a circumstellar habitable zone (CHZ) is the zone around a star with this potential. The concept was introduced in 1953 but the single criteria of ability to hold liquid water is now considered less decisive, and the term liquid water zone and liquid water habitable zone are sometimes more specifically used, and additional criteria such as for the size/frequency of stellar flares, etc., is sometimes included in a more-precisely-defined habitable zone.
A liquid-water habitable zone is obviously bounded by the system's snow line. Regarding the solar system, studies vary in their determination of boundaries, but the region from Venus to Mars is considered a rough approximation. A rocky planet's (long) occupation of a habitable zone clearly does not guarantee habitability: the Moon is virtually a rocky planet and basically as old as Earth, but far from habitable.
The term galactic habitable zone has been used for a region of a galaxy suited to life as we know it, i.e., sufficient metallicity, and an advantageous number of catastrophic events, i.e., supernovae, gamma-ray bursts, etc. Some history of supernovae may be an advantage by contributing to metallicity and star formation.
The amount of received radiation (i.e., the products of radioactivity: alpha, beta, and gamma "rays") has been considered regarding habitable zones: a little to assist evolution through mutation but not enough to prevent development. To me, this seems particularly oriented toward the sort of life found on Earth.
An interesting development of the habitable zone concept is the fact that within the solar system, more bodies have a temperature conducive to liquid water due to their tidal heating than have it due to their distance from the Sun. Moons of giant planets may well be very likely places to find life around other stars, rather than a planet in its habitable zone.