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I think it was originally supposed to mean 'Long Player', back in the days when vinyl was reigning supreme as format of the masses. Bands would release 7" and the like. When they released an album that played for around 40 mins. or so, it was called an LP, or Long Player. These days it is more in reference to a vinyl release. I think. Sounds good to me!
 
"LP" - Long Player. Full 12 inch diameter vinyl album.
As opposed to "EP" - "Extended Play". 12 inch diameter as well, but normally only 4-5 tracks (extended single if you will).
"Single" - what it says on the tin, Also known as a 7" or 7 inch - normally one song on one side, 1-3 songs on the other side.

And yes these are al vinyl - oh how quickly everyone forgets.... but then I'm an old bastard who didn't own a CD until about 8 years ago, and still has about 1000 LPs.....