Many non classical musicians use other notations. For example, many guitarists and bassists use tab notation. It's simply a visual representation of the strings and a number for which fret to play.
It's not as expressive but is far easier to get started with.
MOST guitar players I know use tabs. Personally, I'd rather see the chord type and root string. Ie. 6th string AMin, 4th string GMaj7. Tabs are almost as confusing because I memorized the notes, not the fret number.
I memorize chord progressions in terms of interval-number. E.g. {F# m; B dom7; E Maj} becomes {ii; V7; I}. I've memorized which intervals are major chords and which intervals are minor chords. So if I can figure out the tonic, then I can figure out the key. And if I figure out the key, I need only remember a pattern of ordinals (modulo non-triads).
This is a great illustration of how we grapple with the abstraction of scales and key over time.
First, you have tabs, which describe the physical position of the notes on the instrument.
Then, we have root / chord type notation, in which we describe the starting position and shape of the notes on the instrument, and the musician must translate that information to the physical position of the notes, on the fly.
What is important about this second stage is that the musician has a pretty good grasp on how to play, and can usually sight read a piece and get a pretty decent version of it just by tracking chords, or in the case of the piano, just chords and the melody on the other hand, or a small pattern.
Finally, we come to roman numeral notation, which describes the chords based on their relative position to the root note of key, not the chord. This is a powerful abstraction. It provides incredible insight into the relationships between music, notes, chords, and progressions of chords at a level divorced from the 'root' of that key. A 9th played over a minor 7th chord is going to give you a very similar sound in any key. This is a great skill for songwriters and composers, who need to have a strong working intuition about things like what chord will sound good in this progression, or what notes we want to appear in our melody (which is related to the chords beneath it).
Have you ever used Guitar Pro or Tux Guitar? It can be INSANELY expressive. Grab a MIDI of Van Halen's "Jump" (IIRC The best one was about 76kB) and import it into either of those. Guitar Pro will be noticeably more expressive vs TuxGuitar. Inside of that MIDI, the solo is 100% dead-on note-for-harmonic-for-slide-for-hammer. Both programs output the exact same tablature. You will get the solo perfect.
Most people that have read tablature haven't read the guitar-specialized notation found in Guitar Pro or TuxGuitar. It's far more instructive.
MIDI isn't tab though. It requires note velocities and durations for a start, which tab doesn't. You can go from MIDI to tab but you couldn't go from tab to MIDI.
"MIDI isn't tab though. It requires note velocities and durations for a start, which tab doesn't."
This is entirely incorrect. You can get velocities (Mezzo-forte, mezzo-piano, etc.) and such is expressed if you hover over the note itself in Guitar Pro or Tuxguitar. Sure they change the granularity of it, but the general range remains the same and for all practical purposes sounds the same if played properly.
It's not as expressive but is far easier to get started with.