Why does the immutable version in the following example work, but the mutable version does not compile with error error: lifetime may not live long enough?

trait Car {
    fn honk(&self);
}

struct CarCollection {
    cars: HashMap<usize, Box<dyn Car>>,
}

impl CarCollection {
    // Does compile
    fn get(&self, id: usize) -> Option<&dyn Car> {
        self.cars.get(&id).map(|c| c.as_ref())
    }

    // Does not compile
    fn get_mut(&mut self, id: usize) -> Option<&mut dyn Car> {
        self.cars.get_mut(&id).map(|c| c.as_mut())
    }
}

I know I can work around this issue with:

if let Some(car) = self.cars.get_mut(id) {
    Some(car.as_mut())
} else {
    None
}

But nonetheless, I am really confused by this an would like to know, what is going on here? I thought lifetimes do not differ between mutable and immutable references.