First, some basics:

In classical music, a Composer will write a Work.

This work is then performed by Artists, which can be Conductors, Ensembles, and/or Soloists.
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If this performance is recorded, that's what we call a Recording.
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When a recording is published, it is usually published in the form of an Album.
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Now here's the interesting part: The same recording can be published as part of several different albums, which is why we differentiate between the two.

For example, this recording of Mozart's Divertimento No. 2 in D major from 1986 is featured on two different albums: once on this album collecting different concerti and divertimenti, and once on this compilation album celebrating Mozart's 225 year anniversary.