Time is one of the words that musicians use and misuse routinely allowing for little nuance in its application. Actually it exists on so many levels simultaneously that it is almost impossible to isolate them.
One of the best examples of how it works was given by Hindemith in his wonderful book on the elements of music. He likened the beat to a line drawn on a piece of wood to be cut by a saw: should the blade be aimed inside, outside, or dead-center of the line. Everyone who has ever had a piece of wood cut on the wrong side of the line knows what a difference it can make.
The great accompanist Gerald Moore made an edition of Schubert songs which consists entirely of arrows pointing forward and backward of the "lines."
But there is another level, so fleeting as to almost escape recognition: that nano-instant in which the first vibration hits the ear and occasions a response that will determine the length of the tone, its release, and the touch adjustments to the succeeding tone.
It is the level of time most vivid to me when I play and I am confident that this is what keeps listeners engaged.