Gunite or ShotCrete is the concrete shell that encases the rebar and forms your pool. The plaster is the waterproof layer that contains your water in the pool and give it a nice smooth finish. So if you have a cementous based in ground pool, you probably have both gunite and plaster pool.
Yes, Plaster, whether it contains Pebble, or crushed Quartz/Quartz sand is just the coating layer that covers any Gunite or ShotCrete pool shell. If you get us a close shot of the steps with calm water, we can tell you if it looks to be plain plaster, Quartz, or Pebble...if you dont know that is.
Ok. That clears it up a lot. Pretty sure it's plaster over gunite because it's an old pool made before all the newer finishes came out. It's just smooth and white. I will get a close up pic and post soon.