I've seen a few of your post where you've been trying to tackle the beast that is OpenGL. As the wiki says, pure OpenGL calls mean trouble and are the kind of "confusing mess Processing is trying to insulate you from". If you want to understand how opengl work under processing you should look under the hood. Luckily you can because Processing is open source! In other words, the best thing you can do is take a look at all the important files in Processing's GitHub repo.

Personally I also want to dive further into OpenGL at some point. So I have been taken a look now and then. People have recommended the OpenGL SuperBible (4th) to me as a good starting point for OpenGL. So I plan on buying it soon. With the disclaimer that I haven't taken the plunge quite yet, here are some thoughts on the matter (someone feel free to correct me if I am mistaken)...

In Processing's PApplet the public variable g is the main PGraphics

When you are using P3D this means g is an instance of PGraphics3D

PGraphics3D extends PGraphicsOpenGL

PGraphicsOpenGL extends PGraphics

PGL is the interface between Processing and OpenGL (aka a Processing-OpenGL abstraction layer)

pgl is the public instance of PGL inside PGraphicsOpenGL

In previous versions of Processing (read: 1.5.1.) direct access to the real OpenGL context was done via GL.

However Processing 2.0xx uses a newer version of JOGL and/or uses OpenGL ES 2.0 specifications, which means there are distinctions (especially on Android) between GL and GL2 for direct access to OpenGL methods.

In the end this means that some methods may work with PGL (because they are implemented in Processing's convenience abstraction layer), some will require GL and some will require GL2. In addition some methods are static so can be called via PGL / GL / GL2 while some are not so they need to be called via an actual instance such as pgl / gl / gl2.

So far my $0.02.

thanks a lot amnon ! I have to practice all of this to make android adaptation of those concepts.
for instance find an equivalent of  gl = pgl.gl.getGL().getGL2();- or GL gl GL2 gl2- I have to keep searching !
I'll post my progress (or not progress )
merci

displaying a simple texture shouldn't be sor hard, isn't it ?

To answer the base question: PGL is the name of the class, pgl is probably an instance of this class.
Things prefixed with PGL (or GL) can be only static fields (often constants) and methods (pure functions, working only on their parameters, or on static fields). These things are common to all instances of PGL.
Things prefixed with pgl are only working on the current instance, ie. they are isolated from other instances of PGL.

Not sure if that help, but I hope it clarifies the topic. If not, don't hesitate to ask.