I don't think there is any difference between a vamp and a bed, and they're the same thing. In much the same way as an "aston" could be called a "super".
Here are a few examples from News 24 and Sky News:
N24: Bed/Vamp
- Used at the top of the hour, before the main titles.
N24: Sting
- Used at half past the hour, after the weather and trails.
Sky News: Bed/Vamp
- Used at the top of the hour, after main titles.
Sky News: Sting
- Used occasionally into/out of ad breaks.
As has been said, a sting is general a shorter version of the main theme, used to separate segments of parts of a programme, news, weather, sport etc. Hope that helps.