It doesn't necessarily have to be equivalent to 'P'.
If your camera has a through-the-lens meter, then Shutter-priority or Aperture-priority auto-exposure mode, or Program mode, or metered-Manual mode all use a reflected-light meter reading.
In a Program mode, cameras often have a program-shift function, where you can use the program, but bias it to favour a fast shutter at the expense of aperture more than the default program would; or the opposite, favouring stopping down at the expense of a slower shutter.
Then there's more variation available in how a TTL reflected-light reading is distributed across the frame: spot, centre-weighted average, etc.
I remember there being an accessory you could buy that's a diffuser-dome to fit the front of a standard lens, that even allows you to use the TTL meter for incident-light readings (fit the dome, and point the camera away from your scene, toward the light, to meter before taking your photo in manual). I think it must have been the 80s when I saw that. I never bought one.
Not all cameras have a through-the-lens meter. In some the meter cell just looks forwards off the face of the camera. That's still a reflected-light reading, unless it has a diffuser attachment for incident readings.