Let's look at how to learn to play a part from a popular song. We can get the notes right, but sometimes it still does not sound exactly like the original player's version. The nuances are not there, and that is often what attracted us to learn the part in the first place.
We can fix that problem.
THINKING PROBLEM
Thinking about everything you are doing physically as separate elements while playing a learned part puts things out of synch. That problem is typically caused by the process we used to learn the song. Trying to learn up to tempo because the backing track is fun to play along with - and your skills are "so close" to accomplishing at the "real world" level - will cause a hindrance to improving your personal skills. It's best to avoid "close enough" and really break down the music you are learning.
SYNCHED UP
We want to be in synch as we play, which is learned through meticulous (and sometimes tedious) study of the physical elements needed to perfect the parts we want to imitate. We have access to "Slow Downers" to help us with this. When I was starting out, I had to put my turntable from 33 1/3 to 16 (half speed and all of the notes dropped an octave). I did that until I could get everything at that speed synched up and memorized.
SLOWED DOWN
Once memorized, I sped it up gradually using a metronome until I had it in my wheelhouse. At that point, I played along to the record and it sounded like the session guys: Buddy, Hal, Weldon, Lloyd or whoever I was memorizing for the band's gig requirements. Going to 1/2 speed was my only choice. Technology has made it so that everyone can slow things down to the speed where everything can be easily synchronized and the pitch stays the same. I would have killed for that technology in my day! My advice is to utilize today's technology while also sticking to the old ways of memorizing towards perfection.
MINDSET CHANGE
This is just a "mindset change" towards "how best to learn" - that's all! It's a mistake trying to memorize parts up to tempo - with all of the nuance we will also need to perfect the part. We must get all the details and skills needed... and those have to be worked on slowly and exactly. When rushing up to tempo before we are ready, we are now memorizing and embedding all of the flaws or missed elements into our memory process. We have taught ourselves to play it incorrectly, and to truly master the part, we'll need to waste time unlearning it. Listening critically, you can hear players who choose not to unlearn the bad habits, there is always something a little off about the parts they are copying.
ADDED BENEFIT The benefit of copying parts this way also shows up when we play our own original parts. We have taught our selves how to learn correctly and all of those skills acquired in copying are within us to draw upon when we create. Pedal squeezes, vibrato, rhythmic phrasing, bar moves versus pedal moves, pulling tone, choosing harmonies...all of the details we learned copying are in our muscles and memory, waiting to be combined in new ways.
EMOTION
The purpose of retaining muscle memory is to get it perfect with all of the nuance possible at each stage of our journey. Only allow perfection and exactness to be memorized. Become a perfectionist as we learn, not "learn and hope perfection mysteriously shows up", because it never does. I learned that first-hand many times. The notes of a copied part are just 50% of what is done. The nuance, whether its played by Lloyd Green, Dan Dugmore, or Tommy White, is always what sells the part. Nuance makes the part emote and connect to the listener. Without the emotion, the exact notes are cold and heartless.
DECIDE TO BE PERFECT
Travel the entire road to learning the instrument, never accept less than "The Most Perfect Player" living inside you, and express your love of the instrument and mostly the love of music. Listen deeply, over and over, to the players you copy - after you get the notes - to learn what nuances you missed, so your version can speak as great - if not greater - than the one you copied, because that is also possible if you take this learning path. MIND GAINS
This is something that is difficult for teachers to get across to their students. We can't give you exercises to show you how to listen or force you to slow down to recognize and learn nuance, we can only suggest it, and through our years of experience, describe the results we know you'll get if you follow our advice. It is by you crafting your learner's mindset to allow yourself to embrace these concepts that will give you the skills. Skills that will set you apart from those who learn it only as "notes by rote".