Well, they are not mutually exclusive, but the defaults are very different, i.e., what to do if the compiler fails to assign unambiguous types to all expressions:
- Static: Reject the program, e.g., giving some typing error
- Dynamic: Let it run anyways and see what will happen at runtime
Also, the type-inference of the Julia compiler is comparably simple as it mainly needs to work out the types starting from some specific call, i.e., with specific concrete types as input, and can just give up, i.e., infer Any, if in doubt. In contrast, for a statically typed language it would be rather annoying to reject all but the simplest programs and accordingly type systems have become considerably more complex, handling parametric types, trait bounds, higher-kinded types and what not.