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The term low mass star (or lowmass star, occasionally abbreviated as LMS) is sometimes used in papers and presentations, with varying criteria. Sometimes is use for red dwarfs, e.g., any star less than 0.5 solar mass, but sometimes it is meant to include the Sun, e.g., 2 solar masses and less, in which case red dwarfs might be termed very low mass stars. Likely the terminology depends upon what aspect of stellar evolution or star formation is the subject.
Less mass means dimmer and a longer lifetime, and for stars below 1/2 solar mass, the lifetime is longer than the age of the universe. They are thought to be fully convective, with their helium mixed throughout, and it is thought they will become helium white dwarfs, but without passing through a red-giant stage.
Stars on the order of the size of Sun do become red giants, then eventually white dwarfs.