What is the difference between on-the-go, save episode and download episode?
On-The-Go will create a play list which can be found under My Stations / On-The-Go.

Save Episode will save an episode that you've already played under the Saved tab.

Doing Download Episode, on the other hand, will actually start to download the episode and move it into My Podcasts list.

So, while On-The-Go and Save Episode is a way of organizing the episodes you've already downloaded, doing Download Episode actually downloads it.