APlayer is for playing audio files in the MP3 format.
VPlayer is for playing sound films in the MP4 and FLV formats.
APlayer and VPlayer are both written by the author of media9. They are simple, but provide everything needed for video and audio playback: Play/Pause/Resume via mouse-button press/release or pressing the keyboard space bar, forwards and backwards seeking and volume control via arrow keys on the keyboard, rewind and seek-to-end with the Home and End keys on the keyboard. Moreover, they have a JavaScript interface that can be used with buttons embedded into the PDF (\mediabutton macro). One use of such a button might be changing the media file to be played (by re-setting the source property), another one to seek to a given time in the media file.
StrobeMediaPlayback is a third party, open-source media (MP4, FLV, MP3) player with control buttons, but without JavaScript API and without keyboard controls. On the net, there is a number of other media players available (e. g. FlowPlayer) adding more or less eye-candy. Some of them also have a JavaScript API, but again no keyboard controls in general.
To summarize: If clickable buttons and sliders are desired, use Strobe or another third-party player. APlayer and VPlayer will usually do well, especially in a lecture situation where precise manipulations with the mouse are difficult.