Accurate Physically Based Rendering means that the way the image colors are computed is based on the real world physics. It’s a way to make everything look more photo-realistic/natural-looking by changing how light bounces off of everything.
On the other side, the terms Physically Based Rendering mean that some physical rules are applied but some emphasis on the real-time aspect and the visual appearance of its output rather than the techniques used to achieve it. Anything goes, basically, as long as the final image looks nice. In some situations, there is no attempt to use physically realistic values for the light sources or the surface reflectances. In fact, the light sources themselves often have physically impossible characteristics like 1/r fall-off (as opposed to 1/r^2) or there is a lot of ambient lighting that comes from nowhere but somehow manages to illuminate the room.
Such numerical shortcuts (S-PBR) are often just conveniences provided to the user, so they can get results easily and quickly without having to worry about fussy details, like where to put the light sources and what to use for reflectances. As you might expect, there is a penalty paid besides meaningless values, and that is fake-looking images.
Accurate Physically Based Rendering (A-PCR), on the other hand, follows the physical behavior of light as closely as possible in an effort to predict what the final appearance of a design will be. This is not an artist’s conception anymore, it is a numerical simulation. The light sources start in the calculation by emitting with a specific distribution, and the simulation computes the reflections between surfaces until the solution converges.
Visual Designer 3D, in contrast to most photo-realistic methods, uses a “path tracing” based approach to follow the light. This has significant advantages when the scene geometry is complex and permits the modeling of some complex interactions between surfaces.