What does a streaming application do when I switch from mobile data to wifi? If I am watching/listening to streamed video/audio whilst on mobile data and then become  connected to a wireless network, what does my phone do? 

Does it keep streaming through mobile data or does it switch to wireless? Or is this something that's different across different applications.

My phone is a Galaxy S3, running Jellybean stock.
Usually recent versions of Android Handles these network switching automatically. When you are connected to WIFI, Your content would be streamed via WIFI connection .You can confirm this The mobile network symbol - H/H+/E/4g would not be available in the status bar of the mobile.

Usually, Android manages WIFI and Mobile network automatically, I.e., when both WIFI and Mobile Internet is enabled and If WIFI is avaialble, Mobile internet is not used. When  u leave the WIFI network, you would get connected via Mobile data. Hope this helps :)