'Normal' MPEG streams (which usually have a .mpg file extension) are 'multiplexed' files with a video stream and (at least one) audio stream. These also contain Presentation Time Stamp information (PTS) so the decoder can sync the video and audio together correctly on playback.
For MPEG-2 these are either 'Program' streams (the common variety) or 'Transport' streams (used for digital TV broadcasting mainly). The MPEG-1 equivalent is a 'System' stream.
'Elementary' streams are video or audio only. If you take a 'Program' stream file and run it through a 'demultiplexing' tool it will generate an elementary video file and an elementary audio file by pulling the stream apart. You can reverse the process using a 'multiplexing' tool (TMPGEnc has these tools if you want to try this).