The difference is that in C you can't make a "safe" interface, which the compiler will enforce is used properly.
C's type system is not nearly expressive enough for this. You can barely declare a pointer non-null with extensions, but you can't express ownership. You can't force callers of your function to check for error before using the returned value. You can't force correct lifecycle of objects (e.g. Rust can have methods that can be called once, and no more, and then statically forbid further uses of the object. Great for cleanup without double-free.)
C doesn't have ability to turn off Undefined Behavior for a section of code. You can't just forbid dangling pointers.
For a foolproof API the best you can do is use handles and opaque objects, and a ton of run-time defenses. But in Rust that is unnecessary. Use of the API can be guaranteed safe, and a lot of that is guaranteed at compile time, with zero run-time overhead.
For example, a mutable slice in Rust (a buffer) has a guarantee that the pointer is not null, is a valid allocation for the length of the slice, is aligned, points to initialized memory, is not aliased with any other pointer, and will not be freed for as long as you use it. And the compiler enforces that the safe Rust code can't break these guarantees, even if it's awful code written by the most incompetent amateur while drunk. And at run time this is still just a pointer and a length.
In C you don't get this compartmentalization and low- or zero-overhead layering. Instead of unsafe + actually enforced safe, you have unsafe + more unsafe.