Although the phrasing may not convey it perfectly, the distinction clearly meant is the aforementioned one between the stimulus and the perception of it. The intensity at which a stimulus (e.g., heat, pressure) begins to evoke pain is thus called by a separate term, "threshold intensity". So, if a hotplate on a person's skin begins to hurt at 42 °C (107 °F), that is the "pain threshold temperature" for that bit of skin at that time. It is not the pain threshold (which is internal/subjective) but the temperature at which the pain threshold was crossed (which is external/objective).