I'd say the biggest differences are (a) Rust is more functional (preferring algebraic data types over OO, pattern matching, immutability by default, typeclasses over templates); (b) Rust is newer and younger; (c) Rust has safe manual memory management, enforcing memory safety even if the GC is not used. Of these, I think (c) is the most fundamental difference: it gives the language a very different feel and niche, at the cost of a learning curve.

(Disclaimer: I work on Rust, among other things.)