The Big Difference
From day one, my focus is on your musical fluency rather than all that 'stave notation' sheet music (dots on lines), or constant relience on TAB.
The basic reason for this? Requirement.
The nature of the music that the typical classical piano/violin/guitar player takes on has the following traits; 5 to 20 minutes of continually changing music that a junior player may have never even heard before.
This requires fluent reading of stave notation and training to take lead from a conductor with a wand to hold everyone tight.
You don't play your own music there and if you put your own little twist on the piece you'll be shown to door.
The Stagewise Approach
The common nature of popular-rock music is to take a few catchy 2, 4 or 8 bar riffs or chord sets, repeat as verse/chorus/bridge for 3-4 minutes*, and make your own solo. Each player usualy has a unique part in the song so is free to warp it rather than mirror another player note-for-note.
You want to be able to play off by heart without being fixed to paper, able to recognise and react to changes in the music which then gives you the skill to interact with the band, continuously try new adjustments to your own tunes or covers, make a bit of a stage show of it, or even sing while you're at it.
Relevant Respect to those who role off 20 minutes of music they don't know, but that's the big difference: Instructions to fingers or Ears wired to brains. Hendrix? Lennon? Cobain? What do you reckon?
*Non-repetetive longer songs are called "Progressive Rock" (Prog-Rock), such as Bohemian Rhapsody, Paranoid Android and typicaly a lot of Pink Floyd.