This isn't really a Trinity anymore, because OS - AL - UE became more fragmented. Also, not very coherently presented. Ah, well, don't expect nothing for free.
OS
Operating Systmem. This does the low-level stuff, and includes the Device Drivers.
UE vs. UI
The user environment sets the philosophy for the system. For Windows, this is the GUI. For UNIX/Linux/BSD, this is the CLI. The implementaion of the UE involves the UI, but as a component of a set of default tools. This "sets up" the "flavour" which others follow.
Each Application can "tow the line" and follow the UI conventions set by the OS-bundled applications; or can implement its own style of User-friendly Environment.
AL
Application layer. This is API or system call structure, libraries, upon which useful interactive entities can be build.
e.g. the Win32 API, the MFC, DirectX, OpenGL, VC++ stdcall calling conventions
This layer has the API as the floor, or platform, and the applications themselves as the body, or instances (implementations, programs and libraries) of Application-ness.
PL2
The Programming Language Layer
Application subset: Development tools (used to make more applications).
e.g. Visual C++, Visual Basic, Java Development Kit, Emacs + Gnu C Compiler / GCC.
The Programming Language is actually a whole platform, or virtual machine language. This language is made to be more human-friends, and is generally layered in Core and Library symantics. The Core symantic provide the mechanisms for expression, and the Library provides the frame of reference within which the user generally prefers to operate.
The specific tools used to implement the Development Environment also act to shape the mindset of the artisan (or script kiddy, or cut-and-paster), but enforcing and encouraging certain types of behaviour (such as indenting, explicit #include statements, being pedantic abotu syntax).
K31. 13 Jan. +3.