Reference parameter (&) with and without const in C++

So I was writing a program yesterday, and I encountered a problem that when I use a reference without const, it'll be an error whenever I tried to call that function later. For example:

bool is_vowel(const string& s) //OK;
bool is_vowel(string& s) //Error!
{
    if (s == "A" || s == "a") return true;
    if (s == "E" || s == "e") return true;
    if (s == "I" || s == "i") return true;
    if (s == "O" || s == "o") return true;
    if (s == "U" || s == "u") return true;
    if (s == "Y" || s == "y") return true;

    return false;
}

And considering the following that calls this function: (for simplicity, I've cut out a huge chunk of the original code, so don't focus on the logic here)

int FRI_Syllables(const string& s)
{
    int syllables = 0;

    for (int n = 0; n < s.length(); n++)
        if (is_vowel(s.substr(n, 1)))
            syllables ++;
}

return syllables;

}

So when I use this function, the line that calls is_vowel when I don't use const will return a compile-time error saying "No matching function for call to 'is_vowel'".

I know why references with const here works; what I don't understand is why the one without doesn't.

And another thing that makes me more confusing is that in the FRI_Syllables function, the references work with AND without the const. So considering a part of the code in the main function that calls this function:

int main()
{
    //rest of the code

    int syllables = 0;
    for (int i = 0; i < words.size(); i++)
        syllables += FRI_Syllables(words[i]);

    //rest of the code
}

This won't return any error whether I use int FRI_Syllables(const string& s) or int FRI_Syllables(string& s). So why the differences? Why would references without const sometimes work and others don't?