Re-Writing
Both music and lyrics can benefit from being left for a day or so and then being re-visited later with a fresh pair of eyes - and a fresh pair of ears. I honestly can't think of anything that I've written that didn't change significantly from the first attempt.
This can involve subtle changes - maybe a change of chord or instrumentation or the change of a single word in lyrics. However, it is much more often quite significant changes both to the music, instrumentation, song structure and lyrics. I have abandonned more songs than I've actually written because they just didn't work at the time I was writing. Rather than getting frustrated at the lack of progress, it's far better to 'park' them and move onto something else. I rarely delete anything, though, as reviewing them, sometimes months later, can inspire some new thought that will get them to work more effectively.
Re-writes happen at different stages. Assuming I'm starting with music: It goes through many changes in the writing process. Sometimes this might be a change of musical phrase involving chord changes or the chords might stay the same and instrumentation changes. Often the song structure will be revised if the song is too long or too short. The tempo might be adjusted several times. There have been several occasions where I've changed time-signature, tempo and instrumentation to come up with a 'finished' piece that barely resembled the original.
Lyrics, similarly, rarely stay as they were first written - sometimes, the re-writes just involve getting rid of superfluous words - such as 'and', 'but', 'I', 'you' and so on. Words might also be changed to aid the lyric's flow. On a couple of songs, I've completely trashed all the lyrics and re-written from scratch.
Once I have what I believe to be a completed piece, it is not uncommon for a song or piece of instrumental music to change after recording. There are lots of reasons for this - It might be that instrumental breaks are needed or it might be that the lyrics are fine but space is needed for the performer to breathe between words. This can commonly happen between the end of a chorus and the start of the next verse. Whilst, nowadays we could use 'drop-in' recording to overcome this in the DAW, if the song were ever to be performed live in future, the singer would struggle. So it's better to solve such issues without relying on recording techniques.
Really, re-writing is a key part of the process and should not be overlooked.