What is the difference between pulse-skipping mode and burst-mode in power converters?
Never heard about "burst-mode". Pulse skipping is a simple method to limit the output voltage / current within the maximum permitted margins. The simplest analogy is a children swing. You push every cycle in resonance as long you have enough amplitude, then you skip pushing until the swing goes lower. In a resonance circuit there is a similar behaviour, if the load is small, the amplitudes grow higher and higher if you continue to pump the energy into a resonant tank. 

EDIT:

A paper describing pulse skipping:

Link