The word "hierarchical" in the name refers to a notable feature of PHIGS: unlike most graphics systems, PHIGS included a scene graph system as a part of the basic standard. Models were built up in a Centralized Structure Store (CSS), a database containing a "world" including both the drawing primitives and their attributes (color, line style, etc.). CSSes could be shared among a number of virtual devices, known under PHIGS as workstations, each of which could contain any number of views.
Displaying graphics on the screen in PHIGS was a three-step process; first the model would be built into a CSS, then a workstation would be created and opened, and finally the model would be connected to the workstation. At that point the workstation would immediately render the model, and any future changes made to the model would instantly be reflected in all applicable workstation views.
PHIGS originally lacked the capability to render illuminated scenes, and was superseded by PHIGS+. PHIGS+ works in essentially the same manner, but added methods for lighting and filling surfaces within a 3D scene. PHIGS+ also introduced more advanced graphics primitives, such as Non-uniform rational B-spline (NURBS) surfaces. An ad hoc ANSI committee was formed around these proposed extensions to PHIGS, changing its name to the more descriptive and (optimistically) extensible name "PHIGS PLUS" -- "PLUS" being a slightly tongue-in-cheek acronym for "Plus Lumière Und Surfaces" (the two major areas of advancement over the base PHIGS standard).
OpenGL, unlike PHIGS, was an immediate-mode rendering system with no "state"; once an object is sent to a view to be rendered it essentially disappears. Changes to the model had to be re-sent into the system and re-rendered, a dramatically different programming mindset. For simple projects, PHIGS was considerably easier to use and work with.
However, OpenGL's "low-level" API allowed the programmer to make dramatic improvements in rendering performance by first examining the data on the CPU-side before trying to send it over the bus to the graphics engine. For instance, the programmer could "cull" the objects by examining which objects were actually visible in the scene, and sending only those objects that would actually end up on the screen. This was kept private in PHIGS, making it much more difficult to tune performance, but enabling tuning to happen "for free" within the PHIGS implementation.
Given the low performance systems of the era and the need for high-performance rendering, OpenGL was generally considered to be much more "powerful" for 3D programming. PHIGS fell into disuse. Version 6.0 of the PEX protocol was designed to support other 3D programming models as well, but did not regain popularity. PEX was mostly removed from XFree86 4.2.x (2002) and finally removed from the X Window System altogether in X11R6.7.0 (April 2004).2
PEX was originally known as the "PHIGS Extension to X"; subsequently referred to as "X3d", whose letters form a rotational variant on the letters "P-E-X" ↩
"X.Org Foundation releases X Window System X11R6.7". https://lwn.net/Articles/79302/ ↩
"ISO/IEC 9592-1:1997". ISO. Retrieved 2017-10-14. https://www.iso.org/standard/29417.html ↩
"ISO/IEC 9592-2:1997". ISO. Retrieved 2017-10-14. https://www.iso.org/standard/29419.html ↩
"ISO/IEC 9593-1:1997". ISO. Retrieved 2017-10-14. https://www.iso.org/standard/29421.html ↩
"ISO/IEC 9593-1:1990". ISO. Retrieved 2017-10-14. https://www.iso.org/standard/17366.html ↩
"ISO/IEC 9593-3:1990". ISO. Retrieved 2017-10-14. https://www.iso.org/standard/17368.html ↩
"ISO/IEC 9593-4:1991". ISO. Retrieved 2017-10-14. https://www.iso.org/standard/17369.html ↩