Doing both is called mixed reality. The only caveat is you see reality through a screen and not normal gasses. The terminology is very common in the XR industry. https://www.interaction-design.org/literature/article/beyond...
AVP is, by all definitions, XR, VR, AR, and mixed reality.
AR with cameras and screens is an implementation detail, with the definition being realtime. You can easily play ping pong with an AVP on.