I'd define a preamp as anything that had active components and that operated at a level of millivolts to a volt or two, designed to present its output to a power amplifier. I'd define a "line stage" as a device that acted on signals at the millivolt level and had no user controls, such that it performed a specific task and that's it. Like a phono preamp with RIAA equalization and no user controls.

But others might define these things differently. I've seen some define "line stage" as being passive. I've seen some use the phrase "passive preamp," which generally meant a few switches and potentiomenters or stepped resistor attenuators used in line where a preamp might be. Lots of different ways people use the same labels, so you mustn't assume that you are sure about a person's meaning unless it's clarified with further description or something.