Linestage vs. Preamplifier....

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Nicely said and the correct answer Lowrider57.  

To different things there is no VS!!!

They are both preamplifiers. Linestage is the term used to describe a preamp without a phono section for the TT/cartridge. So the linestage only accepts line-level components such as CDP, tuner, streamer.
A phonostage (phono preamp) is a dedicated device that accepts the low-level gain of a TT/cartridge and then plugs into a linestage. Some preamps will have a built-in phonostage.

 A preamp has a built in phono preamp. A line stage does not. You can (and is sometimes better) use a separate phone preamp with your line stage. You can choose a separate phono preamp that is an excellent fit for your phono cartridge.  

A linestage has no phono preamp. A preamp may or may not have one. I'm sure there's a lot more to it but that's the simple answer.