UT1 is an angle, i.e. the longitude of the mean Sun projected on the Earth.
The mean Sun is a fictitious Sun with a motion that is averaged in comparison to the real Sun.
UTC is the UT1 angle rounded to a multiple of 1/21600 of a right angle, i.e. the angle corresponding to 1 second of time for something that completes a circle in 1 day.
Because of this rounding, actually a truncation, UT1 = UTC + dUT1, where dUT1 is between 0 and 1 "seconds".
Even if UT1, dUT1 and UTC are expressed in "seconds", these "seconds" are not the unit of time, but like I have said, such a "second" is 1/21600 of a right angle or pi/43200 radian.
Both UT1 and UTC are angles that approximate the longitude of the projection of the Sun on Earth, with various accuracies.
Because the rotation of the Earth, which causes most of the apparent motion of the Sun, is almost uniform, the angle of rotation is almost proportional with the time, so the angle UTC is almost proportional with the time, i.e. with TAI.
Because of the way how the "second" angle used for UT1/UTC is defined, the approximate proportionality becomes an approximate equality of TAI with UTC, but because the equality is only approximate, there is an increasing offset between them.
In the ancient times, the people did not care much about time, but only about the angle of the Sun, which determined when it was light or dark, hot or cold, enabling or preventing various activities.
In modern times with artificial lighting and heating and with many activities that proceed at predictable rates, time has become much more important than the angle of the Sun.
In any case, in all contexts we must be aware that the angle of the Sun and the time are not the same thing, even if they are almost proportional, i.e. almost equal after a change of the measurement unit.
The rate of angular change divided by angle sure as heck sounds like units of time to me. The absolute angle isn't, but the rate of change is, and UTC still tracks with rate of change, with a phase angle we periodically twiddle.
That's like saying a watch or even an atomic clock doesn't measure time, it measures oscillations. It's being pedantic to the point of obtuse.
The mean Sun is a fictitious Sun with a motion that is averaged in comparison to the real Sun.
UTC is the UT1 angle rounded to a multiple of 1/21600 of a right angle, i.e. the angle corresponding to 1 second of time for something that completes a circle in 1 day.
Because of this rounding, actually a truncation, UT1 = UTC + dUT1, where dUT1 is between 0 and 1 "seconds".
Even if UT1, dUT1 and UTC are expressed in "seconds", these "seconds" are not the unit of time, but like I have said, such a "second" is 1/21600 of a right angle or pi/43200 radian.
Both UT1 and UTC are angles that approximate the longitude of the projection of the Sun on Earth, with various accuracies.
Because the rotation of the Earth, which causes most of the apparent motion of the Sun, is almost uniform, the angle of rotation is almost proportional with the time, so the angle UTC is almost proportional with the time, i.e. with TAI.
Because of the way how the "second" angle used for UT1/UTC is defined, the approximate proportionality becomes an approximate equality of TAI with UTC, but because the equality is only approximate, there is an increasing offset between them.
In the ancient times, the people did not care much about time, but only about the angle of the Sun, which determined when it was light or dark, hot or cold, enabling or preventing various activities.
In modern times with artificial lighting and heating and with many activities that proceed at predictable rates, time has become much more important than the angle of the Sun.
In any case, in all contexts we must be aware that the angle of the Sun and the time are not the same thing, even if they are almost proportional, i.e. almost equal after a change of the measurement unit.