I wouldn't say they are very similar. Nix is a fairly barebone functional language, so it does embed fairly straightforwardly into other functional languages (including Nickel, but it's true for Haskell, OCaml, Dhall, Jsonnet, Scala, etc. as well - forgetting about Nix-specific builtins, as long as you have higher-order functions, records and arrays, you have the Nix core).

However, Nickel adds pattern matching and destructuring, reverse application, types, contracts and merging, which I think does lead to a quite different experience in practice. It's a bit like saying that C is similar to Rust (ok, so the analogy doesn't work as well for Rust as most C would be unsafe on non-idiomatic Rust) or C++: in some sense, yes, but developing in those languages is very very different.