Ok, let’s expand on things a little. The reason that it is “total” is that it is the runout due to eccentricity added to the runout due to the job not neccessarily being round. (For instance a piece of centreless ground bar may have a lobed shape rather than being a true circle.) The indicator will measure a amount that depends on all the errors. Practically, when the total indicator runout is minimised, the job is as close as you are going to get to being truly centred. The reading will only be twice the eccentricity in the case where the job is for practical purposes truly circular, which is often, but not always the case.
Andrew, whether or not you are measuring radial or axial runout is going to depend on how you have set up the indicator. Taking say a flywheel shape, if you set up the indicator to read against the outside cylindrical surface you will measure radial runout, while if you set it up against one side you will measure axial runout.
regards
John