typeid vs std::is_same vs if constexpr

I'm confused by these three things. Here is a simple example:

template<typename T>
void func(T t) {
    if (typeid(T) == typeid(int)) {
        std::cout << "f - int" << std::endl;
    } else {
        std::cout << "f - other" << std::endl;
    }
}

template<typename T>
void func2(T t) {
    if (std::is_same<T, int>::value) {
        std::cout << "f2 - int" << std::endl;
    } else {
        std::cout << "f2 - others" << std::endl;
    }
}

template<typename T>
void func3(T t) {
    if constexpr (std::is_same<T, int>::value) {
        std::cout << "f3 - int" << std::endl;
    } else {
        std::cout << "f3 - other" << std::endl;
    }
}

int main() {
    func(1);
    func('a');
    func2(1);
    func2('a');
    func3(1);
    func3('a');

    return 0;
}

The output is

f - int
f - others
f2 - int
f2 - others
f3 - int
f3 - others

So it works as expected. But I kind of don't know which one should be used in which case.

As my understanding, typeid in the first one is totally about runtime. That's all I know. But template is about compile time, right? So does it mean that the func is a stupid design?

How about the func2 and the func3? Are they exactly the same thing? Are they all about compile time? Or the func2 is still about runtime?