Neither one is what one cares about, which is the amount of compression at every point along the perimeter.
Concentricity and runout and total runout do this indirectly and try to control either the variation of variation (concentricity) or variation with respect to a non-functional datum (runout and total runout).
The direct geometric tolerance control for this is profile of line applied at each location around the perimeter with a tangent plane at each location around the perimeter and an alignment to the axis. This control and control of the bore and piston diameters controls the compression of the o-ring directly to ensure it is stretched the correct amount and does not have too much exposure allowing the o-ring to squeeze out.
Gland depth is the control specified by o-ring makers.
www.globaloring.com
No surprise, concentricity, runout, and total runout are not mentioned by the companies that supply o-rings as a geometric tolerance control, though it is mentioned as a conventional English term.
There are groove depth measurement tools. They sit on the tangent plane for external features.
If one looks only at runout or total runout, it is possible to have an out-of-round condition in the cylinder out of phase with an out-of-round condition or being off-center of the o-ring groove, leading to both excessive depth and insufficient depth that would be ambiguous, even if the range of diameters for both features was reported. It would be necessary to measure the groove/gland depth to see if the part was usable.
Concentricity is a worse control for this case than runout and total runout as it does not detect all out-of-round cases.
I don't imagine anyone using total runout on a face seal thought they have the same compression requirements.
This was the previous discussion:
The Parker book is touched on here:
The main concern in the Parker book is as follows:
Runout (Shaft): Same as gyration; when expressed in inches
alone or accompanied by abbreviation “T.I.R.” (total
indicator reading), it refers to twice the radial distance
between shaft axis and axis of rotation
rather than the groove runout to the shaft. This is to control variation in compression as the shaft rotates. It is also mentioned in regards to a special sort of seal between a fitting fillet and a chamfer in a tube fitting boss seal. This makes some sense as there is no "depth" that can be measured on a chamfer. Since there is no further explanation and there is another precise diameter for the o-ring to engage, it might be to simply control the forcing cone action rather than the squeeze.
There is also mention of "*Total indicator reading between groove and adjacent bearing surface." as "Max. Eccentricity," not between the groove diameter and the axis of the entire bearing diameter. They want the compression to be uniform. A uniform compression will avoid the o-ring from trying to creep along the groove away from the high compression zones towards the low compression zones and changing the local o-ring section area in unwanted ways.
It is certainly worthwhile to consider cylindricity on the non-gland/groove surfaces involved and runout if there are guide bearings to locate one part relative to the other, but for the o-ring gland/groove the makers of o-rings appear unanimous in not using geometric tolerance symbols or referring to standards for them. But this isn't the forum for their nonsense.