In both cases, you need to download the same number of bytes, but streaming takes them at a much slower rate, thus using less bandwidth (which is measured in terms of data divided by time).
When streaming a podcast, you need to download a minute's worth of audio every minute, plus slightly more for buffering.
Given that it doesn't take an hour to download an hour long podcast, you are getting far more data per minute when downloading than you are when streaming.
To put it differently, if you're streaming an hour-long podcast, you are guaranteed to be transferring only that one podcast over the network during the next hour -- and if you stop and move on to something else, you stop downloading that podcast.
If you're downloading an hour-long podcast, you might download several of them during a one hour period, putting much higher demand on the network.