A progressive download will be downloaded to your computer and stored in the cache. Generally you can tell by watching the progress bar getting longer as more of the video is being downloaded.
A streaming download is downloaded in small chunks to your computer. It is not stored in your cache so does save space, but it streams and plays simultaneously.
If you've ever tried watching a video online and before playback (and often during playback) it says "buffering", you know this is a streaming download.
Streaming is often used for live video / broadcast events.
Progressive video can often be higher quality than streaming and are stored on your computer.