The LEFT/RIGHT distinction for the buffers is used for stereo display. For double buffered stereo, you would render the image for the left eye into the GL_BACK_LEFT buffer, the image for the right eye into the GL_BACK_RIGHT buffer, and then swap buffers.
In stereo mode, GL_BACK is used if you want to render the same thing to both GL_BACK_LEFT_ and GL_BACK_RIGHT. Which is quite rare.
You're correct about GL_FRONT_AND_BACK. Rendering to the front buffer is long obsolete, and was only useful in special cases anyway. One typical case was for drawing special cursors, like cross-hair cursors, using OpenGL, on top of an already displayed frame. Rendering to both front and back at the same time was even less useful. I can't think of a good use case right now.
AUX buffers are long deprecated as well. I believe they were intended for rendering effects where you needed additional color buffers. These days, you would use FBOs for the same purpose.