Try the following exercise.
Get two pieces of lined paper and a pen. Sign your name on the top line of the first. Take the second, turn it sideways, stretch out your arm, and sign your name across the second the way you'd sign your name on a chalk-board, with your wrist and elbow stiff.
Compare the two. It's the same signature. Your signature isn't in your muscles, it's in your brain.
In like manner, when you learn a tune it's not in your fingers, it's in your mind. Sing "Happy Birthday." (Yes, out loud.) Now whistle it. Same tune. Same version. Same notes. Different muscles.
Go through the tune in your head once. Same version, again. Replay just the last line in your head. You don't just know it as a stream of notes, you know all the pieces. You can probably hear, hum, or sing, any self-contained piece of it. "You belong in a zoo."
You know this tune.
Learning a tune means having a version in your head, completely, note-for-note. Once it's there, you just play it, with whatever instrument's at hand, well or badly. Some people's handwriting and singing is prettier than others, but we all get by.
Now run get some recordings of tunes you want to learn, and listen to them until they're stuck in your head -- until you can hear them, end-to-end, in your head, without the recording.
