Is there a difference between audio.play() and media.play() and which one is better?
The audio.* API calls use the OpenAL audio layer to play. They are considered a safer and better way to play audio in Corona SDK. You can have 32 different sounds playing at once. You can control the volume on each channel independently, pause and resume, fade in, fade out, etc. It is the preferred way to play sound.
The media.* API calls write directly to the hardware and you cannot control the volume, have multiple sounds going on. The media.* API Calls though are good for video, playing long clips, like podcasts since that audio can be backgrounded, but more importantly, on Android, Google has decided to poorly implement OpenAL and under 4.x there is a significant lag from the time you tell audio.play() to play a sound and it really happening. The lag isn't as bad under 2.2 and 2.3, but there still is a lag. The media.* api calls, if you're playing a short clip will play in a timely fashion.