My new mp3 player has no Pause button, or maybe it has no Stop button. This omission is so interesting that the manufacturer addresses it in the player's online FAQ.
CD players can both stop and pause.
DVD players can both stop and pause.
Tape machines can usually both stop and pause.
Record players can stop (lift the needle off the record) and, pause, sort of (raise the cueing bar, you might be able to set the needle back down in the same place was later).
So why is there only one button now, that works for both stopping and pausing? The answer's pretty obvious: older audio players distinguish between these functions because of a technological tradeoff, not because we users want both functions. On a tape player, leaving the unit paused for quick resume is convenient, but leaving a tape in pause a long time uses electricity and can wear out the tape. On a CD or DVD player, the “pause” command supports a quick resume where you left off, consuming extra electricity and – maybe – wearing out the mechanical arm that positions the laser. The manufacturers recognize there's a tradeoff, and they make US decide whether to stop or pause, instead of making a manufacturing decision to support only one of the two alternatives.
On my mp3 player, there's always a quick startup, as long as the player's on (or even “mostly on”). So there's no tradeoff, and no need for two buttons. Instead, there's one button with the well-recognized play/pause icon, but it's actually a play/stop button.