I found two most popular (number of installations) Clojure extensions to VS Code:
Both are maintained but Calva seams to have more attention. Both are aimed to help to integrate Clojure (and ClojueScript) to VS Code users.
It is unclear to me if they are complementary to each other or there are "do the same thing" but differently?
How are these two tools related to each other?
So, those two extensions are best thought of as competitors. They basically ”do the same thing”, as you put it. In reality it is a bit more complicated than that, but in any case you have to choose between one or the other. The overlap is greatest in the interactive programming department, both hook VS Code on the power of the REPL.
I can only speak about Calva really, because I am the maintainer of it. Calva is moving in the direction of packing more than just the REPL connection in one extension. Today it does that by bundling Calva Formatter and Calva Paredit, but a few releases from now it will all be in just one extension.
I think the reason Calva has more attention is that I am a very active maintainer. Andrey still maintains the Clojure extension, but it seems it is quite seldom and mainly to keep it working as stuff around it changes. Lately, I have also gotten a lot of help and we have gained the power of adding some really big things, that will soon be released. My guess is that Calva will soon become the only reasonable option for quite a while. (But, yes, I am biased.)
Let me take this opportunity to invite people interested in, or in need of support of, Calva to the #calva-dev channel of the Clojurians Slack.