David,
I'm not aware of any definition of what counts, but it is certainly the case that a BFR or club checkout does not count, i.e. you can do that on a Visa Waiver without a Visa. Someone posted a link to the relevant part of the US Immigration services website long long ago which made that clear, but I'm afraid I don't have a clue where the link is. Bearing this in mind, your example of sitting in the left seat and having the instructor endorse your logbook is not sufficient to require a Visa.
My own interpretation is that you need a Visa if the training you are doing will count towards the required training hours for any Licence or Rating, e.g. PPL, CPL, IR, IMC, type rating, class rating and so on. But, as I've said many times, neither my interpretation nor anything that anyone has written actually make any difference at all - the only thing which counts is the way the immigration officer on duty the day you arrive interprets the rules (and this may depend which side of bed he got out of and whether the milk in his morning cup of coffee had gone sour). If he decides that you're breaking the law, there is no means of appeal - you will be sent home.
FFF
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PS - Agree with Keygrip's edit to my first post, unless you want to take pax flying in which case a student pilot certificate is not enough