Dave, in the context of the Internet, the garden and the stream are metaphors for two different approaches to content on the Internet. A stream is ephemeral, it continues to move over time and one mostly adds to it and watches it flow away. On the Internet a stream is content for only right now, and usually isn’t edited nor looked at years later. Streams are date and time driven. Stream platforms are optimized for quick and easy entry of new content.
Twitter, Facebook, and blogs are examples of platforms used for publishing streams of content. Note that this is not absolute, for example one can and might edit a blog post they wrote a year ago in which case that blog might well be a garden.
The garden metaphor, in contrast, is more permanent. The content in a garden is continually edited to reflect new ideas or new learning over a period of time. A garden is organized around a topic. Platforms for creating and maintaining gardens are optimized for editing and linking together of content. Connecting the dots (linking) between content can generate new ideas or thoughts. Wiki is an example of a garden platform, as is the web itself as originally intended, as are other tools optimized for linking together and organizing content.
A couple of other interesting differences exist between the two from a user and platform provider perspective. Almost all streams are public, their very point is public sharing, and the platform providers freely provide their platforms and make their money my manipulating the presentation of what one puts in to the stream to others. Users have little to no control over who sees what they put in to the stream.
Gardens are either public or private, thus users tend to have more control over who and how one sees their content. Platform providers either freely provide their platform as open source for users to install in their own computers or they make money by hosting their platforms and charging uses for renting space on their hosting. The key point being the garden platform providers do not make money on the content. In my opinion, a site that has the purpose of making money from content is something other than a garden, so for example, I do not think of Medium as a garden, nor are other sites like The Verge or Engadget that may publish using a blogging or content management system.