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I encountered this issue when searching for a song in my saved songs that was shown as "liked" but I could not find.
I realized that Spotify treats the two apostrophes as different characters. Granted they are, but it makes it unreasonably difficult to search for songs with an apostrophe in the title.
It's difficult to see, but they are different and Spotify is treating them differently.
This results in different song selections depending on if you use the straight quote or use the extra effort to type the "smart" version.
This is happening on both mobile (iOS) and desktop, so it's a Spotify issue rather than OS or platform issue.
I saw another issue that was marked as not enough support to implement, but it suggested having spotify ignore apostrophes altogether when searching which I think would be the best approach to resolve this.