A boiler, as the name suggests, boils the water before turning it into steam at subcritical pressure - the pressure at which bubbles can form. Steam generators, on the other hand, convert water into steam into steam without boiling at a super-critical pressure.
There are also constructional differences between a boiler and a steam generator. A boiler contains many tubes which carry the water. A steam generator has, generally, only one tube in which the heating occurs.
