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The turn-off (TO) point is one tipping point on the Hertzsprung-Russell diagram (HRD) where low-mass stars start to evolve from the main sequence (MS) toward lower temperatures. If I understand it correctly, this is the beginning of the sub-giant phase when the stars no longer have hydrogen burning at the core.

The definition above suggests that the TO point is the same as the terminal age main sequence (TAMS), however, I have not found a source that explicitly states so.

Is the TO point the same as the TAMS?

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TL;DR: Turn Off point (TO) means the location of the "knee" in the HRD of clusters of stars. TAMS is an imaginary line in the HRD that is defined by the location of stars of different mass at the end of hydrogen burning. It constitutes the upper boundary of the main sequence.

More details:

There maybe some confusion because the terms are not completely specific.

A Zero Age Main Sequence star (ZAMS) star is a star that, after formation, has reached hydrostatic equilibrium and just started hydrogen burning. But ZAMS can also mean an imaginary line in the HRD that is formed by the location of all ZAMS stars of different mass. This line constitutes the lower boundary of the main sequence.

A Terminal Age Main Sequence (TAMS) star is a star that has reached the end of hydrogen burning. TAMS can also mean the line in the HRD diagram that constitutes the upper boundary of the main sequence.

The main sequence can thus be considered a band bounded by the ZAMS and the TAMS in which Main Sequence stars may be located. In the following figure (Maeder A., Meynet G., 1989, Astronomy & Astrophysics, 210, p. 155) this band (and other areas of slow development phases) is shown as shaded area:

enter image description here

With time (and hydrogen consumption) a star moves from its ZAMS location (determined by its mass) up and right to its TAMS location. The most massive stars evolve more quickly, reach the TAMS earlier and then move away from the main sequence.

The Turn Off point is only relevant for clusters or groups of stars that formed at the same time. With increasing age of the cluster, its stars move away from the main sequence, starting with the most massive ones in the upper left area, leaving more and more of the upper area of the "band" unoccupied. The TO point can be thought of „sliding down" the TAMS with time. From the position of the TO the age of the cluster can be determined.

https://commons.wikimedia.org/wiki/File:Open_cluster_HR_diagram_ages.gif#/media/File:Open_cluster_HR_diagram_ages.gif

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