When I first started playing music, I would write down just the chords to remember the songs.
Today we have guitar tabs, so you actually know the fingering. And presuming you know the tempo you can work out the tune.
How many of us use to learn songs was we listen to the over and over to learn them by ear
Once I new a song I wrote down the chords and shared them with my friends in high school
To write down the lyrics we would be four guys in the band listening to record. The first guy would write down the first line. The next guy the 2nd and so on. This way you reduced the number of times you had to play the record.
Today you download the tab and lyrics
Many just enter it into their mobile device and take it with them.
How do you remember the songs you play? What about the songs you write?