I think one has to expand a bit on this. Because if you reorder it, people could still think it works fairly well and don't see the problem at all:
artist/album/song
vs.
composer/work/movement
However, the real problem is that in classical music a lot of things have the same names. Movements (= the actual songs) are just a number and a tempo/mood, e.g. "I - Allegro", so thousands have the exact same name in multiple works (imagine pop songs just having the album track number as their only name). Also, composers write works with the same names all the time, e.g. "Symphony No. 1" (imagine every pop singer releasing "Studio Album 1"). And all of these works are played by hundreds of performers/orchestras/conductors, so everything is the same except the performer (imagine hundreds of equally famous song covers). And of course one performer may even have multiple recordings of the same piece. Then there is the chronological enumeration of each composer's works. These can be the same for different composers, e.g. "Op. 27 No. 2" is a Beethoven Sonata and a Chopin Nocturne. Then there are also nick names like "Moonlight Sonata", of course called differently in other languages. Such names can even be the same for multiple pieces by the same composer. For example, Schubert's "Ständchen" (D 889, D 957 No. 4). Finally, a work is often referred to by the key it is written in, like Rachmaninoff's "Prelude in C-sharp minor", which again is called differently in other languages if the original recording was produced for the local market.
To sum it up, names are confusingly generic and it doesn't help that generally a lot of numbers and abbreviations are involved and people make typos (E-flat vs. -sharp, who cares/knows) or are lazy. "Chopin 10" is an Opus number (piano etudes), but "Beethoven 3" is the 3rd symphony, Op. 55.
Presenting this information in a way people can easily find what they need is the big challenge, and it looks like they haven't completely succeeded yet. But in any case, browsing and searching certainly can be made much better if the classical context is known. It therefore makes perfect sense to have its own app.