Real and fake books are skeletons of classic tunes. They're the bare bones - containing minimal information. The basic tune (lead) and the harmonies (chords), sometimes with alternative chords shown. They're really not meant to be any more, any less. They're enough for musicians to have in front of them to play, straight off, any of those tunes.
Because it's mostly jazz, even a simple rendition may deviate from what's written - it's what jazz does - so expecting anything in the Real book to be a faithful copy of any recording is folly. And if one only plays the tune, bare, or the chords, with no melody, well, it's hardly going to sound like a trio or quartet track.
Listen to ten different recordings of, say, Autumn leaves, and you'll recognise the melody (at least first time round!), but then you'll hear ten different - often very different - 'translations' of the piece. All probably initially gleaned from a Real book.
Plus - they're going to sound rather different unless you use the same instrumentation as on tha recording, and maybe - even the same players!