In the classical tradition the piece is written out like this:
But in the popular song tradition we use a notation like this:
It gives us the melody and the chords that go with it. This is the basic notation used by all all musicians in the popular music traditions, from jazz, to folk, pop, rock, you name it. Why?
When you write out a piece in standard notation a) it's more difficult to read; b) it's to be played in one particular way only; c) there's no grasp of the underlying harmony - the movement of the chords that accompany the melody - and therefore no way to know how to color and modify how the piece can be played. Because songs have relatively slow melodies, and chord patterns used to accompany melodies are so standardized, a brief shorthand- the chord symbol - is all the instruction you need. You learn lots of different ways of playing these same chords, and you get to learn them in your hands. Then you begin to find, especially to feel, that the chord movements are very similar from one song to the next. Soon you're less and less dependent upon a chord chart.
The chord chart (along with an understanding of chords, their relations to each other, and how to arrange chords with the melody) is the preferred notation for song playing. When songs are written out in two handed notations, those are usually for the lowest common denominator
reader, with only average reading skills. The arrangements tend to be simple minded. When you work with chords you understand how to enrich song sounds without reading a complex cluster of notes on the staff. The looks of the keyboard becomes your music, as you find chords and assemble their tones in different ways, using rules to modify them to get the kind of sound you want to get. Much more flows out of a chord notation than a two handed, two-staved notation. in the world of popular music and improvisation.