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I don't see any specific evidence given any that good textbook is "inconsistent," merely vague accusations cast without evidence. A straw man.

Affordances have a specific meaning in design. Affordances themselves are subjective because they depend on prior user training. Signifiers are nonessential, supportive adjuncts to affordances to reduce cognitive load (fewer uncertainties and more clarity).

"PUSH" sign on a door that already had a door crash bar facing the observer. A crash bar already indicates it is both a door and opens outwards. A further signifier for a clear wall and door would be a faux door-jam around the perimeter of the door so that people can tell where the door is more easily. If a door blends-in completely to a wall, then any indication of it is an affordance.. it's additional, supportive cues that would signifiers. Putting bright orange around a "PUSH" sign or some aspect of an opaque doorway would likely make it a signifier.

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Human–Computer Interaction, Preece et al. (1994, p. 6): The authors explicitly define perceived affordances as being a subset of all affordances, but another meaning is used later in the same paragraph by talking about "good affordance." Universal Principles of Design, Lidwell, Holden & Butler (2003, p. 20): The authors first explain that round wheels are better suited for rolling than square ones and therefore better afford (i.e. allow) rolling, but later state that a door handle "affords" (i.e. suggests) pulling, but not pushing.