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They're similar! The author of Janet previously wrote https://fennel-lang.org/, a compile-to-Lua language.
Janet has more traditional scoping rules than Lua. Tables and arrays are separate types in Janet, and arrays are 0-indexed. Biggest runtime difference is probably that Janet has value types.
I think the compile-time programming is the real differentiator, but it's hard to summarize what that means in a comment.
Performance is pretty similar to the vanilla Lua interpreter in the benchmarks I've seen and run (Janet typically wins slightly), but there's no LuaJIT.
If you like things like Janet, you might also like s7 Scheme. It is also a minimal Scheme built entirely in C and dead easy to embed. I used it to make Scheme for Max and Scheme for Pd, extensions to the Max and Pd computer music platform to allow scripting them in Scheme. (https://github.com/iainctduncan/scheme-for-max) Janet was one of the options I looked pretty closely at before choosing s7.
The author (Bill Schottstaedt, Stanford CCRMA) is not too interested in making pretty web pages, ha, but the language is great!
Reading Peter Norvig's PAIP (https://github.com/norvig/paip-lisp) in 1998 totally blew my mind. It completely changed how I think about programming in every other language I use(d). I love it still, and always will. And yes, my experience is the same as yours: learning lisp made me a better programmer in every other language I use (especially -- but not only -- Python).
The simplicity and symmetry of the syntax is a big part of that love for me. Being able to manipulate lisp code as lisp data, using the full power of the language to do so, is just brilliant.
Janet looks lovely! Looking forward to the book.