While rendering is the proper term for exporting in After Effects, isn't rendering in Premiere Elements and Premiere Pro preparing the timeline for smooth playback? Isn't sharing the output term in Premiere Elements and exporting the term in Premiere Pro?
Rendering is the process of combining all the tracks, layers, applied effects, etc. into a single composite image. Videos are rendered frame by frame. Encoding is the process of applying a codec to compress the video. So, to export a movie you both render and encode it. We'll come back to this in a moment when we talk about exporting from Premiere Pro and After Effects.
To view the video in the monitor window while editing, you also need to render the video. If the computer is fast enough and has enough resources to do so, it can render and play at speed. If the computer can't keep up, the video playback can hesitate or jump. To provide for smoother playback while editing, Premiere can create temporary preview files. These preview files are rendered and then encoded with a codec that is compatible with the project settings and which is easy to decode and play back. This process is also called rendering and is what happens when you press enter to render in Premiere.
Exporting is the process of outputting the edited project to the desired finished format. Premiere Elements calls this "Sharing". Premiere Pro and After Effects call it exporting and there is an export option in the File menu for this. The most commonly used export option in After Effects is "Add to Render Queue" and there is a keyboard shortcut (ctrl+M) to do that directly. The render queue in After Effects works similar to the Media Encoder that comes with Premiere Pro. When you queue something and start the queue, the rendering and encoding processes are separate. If you specify more than one encoding option it will render once and then encode each output format.