Over time and as we develop as musicians, our ears become more sensitive and we hopefully hear when we're out of tune or playing too fast, or too slow, 'ahead of the beat' or 'behind it', but good musicians listen to what they are playing in relation to their band context and adapt their playing accordingly.
Drummer Jon Christensen says for example:'band feel is more important than bravura’. We’re building our own personally-blended method of listening, playing, reading and getting it right. Everyone learns differently and some people find playing by ear or by the chart much easier than others, we have to do whatever works best for us.
Sax player Dewey Redman tells the story of how Louis Armstrong was once asked if he could read notation and reportedly answered 'yes, but I try not to let it get in the way of the music!' Many fine jazz musicians have struggled to read notation but have played fine music anyway, take Chet Baker, Wes Montgomery and Erroll Garner for example. Even Dave Brubeck faked his way into music college and was nearly thrown out when his limited reading skills were eventually rumbled, but that didn't stop him becoming a masterful player. Some jazz musicians have a strong background in classical training, take Gwilym Simcock for example; some others learn songs by ear and interpret the score in the light of what they hear, others run both approaches alongside each other. Whatever works for you in grasping a piece of music, there's not just one monolithic obligatory approach. Chet Baker once said 'I just learned to play on my own. I like to hear a chord and from what I hear, I respond. I hear something and I try to get it out at the end of the horn'. But whether we use charts or our ears or some blend of both, our aim is get it right in terms of faithfulness to well-crafted original tunes.
For both singers and instrumentalists, it's also important to consider the lyrics of a song, to reflect their meter, mood and and 'backstory' as Rene Marie would put it. Some musicians play 'Autumn Leaves' for example as a cheerful upbeat song with no regard to its core emotional message...'I miss you most of all ....'. Highlight the key emotional heart of a song's lyrics to make sure you really 'get' it.
Next Step: Improvising