Unlike the other platforms mentioned, Apple doesn’t “stream podcasts”. Apple indexes submitted RSS feeds. When you subscribe to a podcast, the player polls your server directly to update the RSS feed. When you play a podcast, it is streamed directly from your server. You can add any RSS feed directly into the player and play it. Apple isn’t involved.
The difference is extremely important. The other services force you to go through their platform. In fact, Apple has provided a freely accessible API to its podcast directory that anyone can use without asking Apple’s permission.