What is the difference between a const variable and a static variable and which should I choose?

Mutability

A const variable in Rust is immutable. You neither can reassign nor modify it:

struct Foo(u32);

const FOO: Foo = Foo(5);

fn main() {
    FOO = Foo(1); //illegal
    FOO.0 = 2; //illegal
}

A static variable can be mutable and therefore can either be modified or reassigned. Note that writing/modifying a global static variable is unsafe and therefore needs an unsafe block:

struct Foo(u32);
static FOO: Foo = Foo(5);
static mut FOO_MUT: Foo = Foo(3);

fn main() {
    unsafe {
        FOO = Foo(1); //illegal
        FOO.0 = 2; //illegal

        FOO_MUT = Foo(1);
        FOO_MUT.0 = 2;
    }
}

Occurrences

When you compile a binary, all const "occurrences" (where you use that const in your source code) will be replaced by that value directly.

statics will have a dedicated section in your binary where they will be placed (the BSS section, see Where are static variables stored in C and C++? for further information).

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All in all, stick to a const whenever possible. When not possible, because you need to initialize a variable later in the program of with non-const methods, use lazy_static!.

There's not much practical difference if your variable isn't intended to change.

Constants are inlined at compilation, which means they're copied to every location they're used, and thus are usually more efficient, while statics refer to a unique location in memory and are more like global variables.

Constants are... constant while statics, while still global, can be mutable.