It looks like for now you'll have to list all tag providers first (see this post for inspiration) and individually export them, then figure out some way to combine the different JSON exports together.
In the script console, the exportTags functions is going through a different code path (first, it hits the implementation of the tag scripting functions, then inside that (on the client) it calls out to the gateway, where it ultimately hits the gateway implementation of exportTags, which is automatically qualified with the project name (and therefore a default tag provider).
The path when issued from WebDev does get automatically qualified with the project name/project default tag provider, but due to a bug in exportTags doesn't get picked up.
I'll make a ticket for this, but it won't be fixed any time soon (and only in 8.3 whenever it does).
From looking at the code I'm pretty sure that exportTags in the script console is giving you everything from the project's default tag provider, not actually every tag in every provider.