Linestage v. Preamp

They are both preamplifiers. A fully configured preamplifier has inputs for various high level sources (CD players, tuners, DVD players, etc...) AND a RIAA phono input. The phono stage in a preamplifier takes the minute signal received from the tonearm lead and amplifies/processes the signal so it can be heard at normal levels.

A linestage is a preamplifier as well, only difference is it does not have a phono input. It accepts "line level" inputs only (CD players, tuners, DVD players, tape decks, etc...). Linestages have become more popular as people (for a time) gave up on vinyl and focused on CD players and whatnot. Since there is no real processing of signals in a linestage (no RIAA circuit), in essence the line stage premaplifier is a volume (gain) control, and control center allowing you to switch between various sources at the push of a button.

What if you have a great linestage and want to take the leap into vinyl? Do you have to sell your premaplifier and find one with a built-in phono section? Nope. You can still use a linestage with a turntable, you need to add a phono pre-preamplifier in the chain. You plug your tunearm lead in to the phono preamp, the phono preamp steps the signal up, and then outputs the now "line level" signal to the preamp. My chain looks like this:

SME tonearm lead => Lehmann Black Cube Phono Preamplifier =>
BAT VK30 Line Stage Preamplifier=> Bat VK500 Amplifier

linestage doesn't have a phono stage vs. a preamp has a phono stage

All preamps once had built-in phonostages, in the days before high-output, non-EQ-needing CD players became the most popular source. Today such preamps, capable of directly handling the signal from a phono cartridge, are called 'full-function', while those without internal phonostages are called linestages. They're all preamplifiers though. BTW, a stand-alone phonostage is sometimes also called a 'head-amp' or a pre-preamplifier, and 'passive preamp' is a bit of an oxymoron - they should rightly be called passive attenuators/switchers, because they don't do any amplifying (real preamps with gain are also referred to as being 'active' in comparison, though this is normally assumed without explicit mention).