I have a very loose grasp of the OpenGL environment, so this is something I'm trying to understand. Could someone explain in lay terms what is the difference between these two styles of rendering? Primarily I would like to understand what it means to render to a texture and when would it be appropriate to choose to do that?
If you render to a texture then the image you've rendered is processed in such a manner as to make it immediately usable as a texture, which in practice usually means with negligible or zero effort from the CPU. You normally render to texture as part of a more complicated rendering pipeline.
Shadow buffers are the most obvious example — they're one way of rendering shadows. You position the camera where the light source would be and render the scene from there so that the final depth information ends up in a texture. You don't show that to the user. For each pixel you do intend to show to the user you work out its distance from the light and where it would appear in the depth map, then check if it is closer or further from the light than whatever was left in the depth map. Hence, with some effort expended on precision issues, you check whether each pixel is 'visible' from the light and hence whether it is lit.
Rendering to a CAEAGLLayer-backed view is a way of producing OpenGL output that UIKit knows how to composite to the screen. So it's the means by which iOS allows you to present your final OpenGL output to the user, within the hierarchy of a normal Cocoa Touch display.