Well, a line stage is often called a preamplifier these days, so that's part of the confusion. In the days when vinyl was the primary source, a preamplifier used to always include both a line stage (to handle line-level sources such as a tuner, CD player, tape deck, etc.) and a phono stage (so you could apply the RIAA equalization to the signal from your turntable/arm/cartridge source and then be able to listen to records) in it. As CD became a more popular medium, preamplifiers started to appear in the market without the phono stage, and these were called line stages. When it became clear that vinyl has refused to die, manufacturers started making separate phono stages to make the RIAA correction and bring the phono signal up to a line level signal in terms of voltage, which could then be connected to your line stage, partially because there are distinct advantages to keeping the phono section apart from the line level circuitry and partially I'd imagine because of tooling, production and marketing reasons.
Given how most people seem to refer to line stages as preamps these days, perhaps the way to describe the old idea of the preamplifier would be to call it a full-function preamplifier.
