Difference between regex_match and regex_search?

I was experimenting with regular expression in trying to make an answer to this question, and found that while regex_match finds a match, regex_search does not.

The following program was compiled with g++ 4.7.1:

#include <regex>
#include <iostream>

int main()
{
    const std::string s = "/home/toto/FILE_mysymbol_EVENT.DAT";
    std::regex rgx(".*FILE_(.+)_EVENT\\.DAT.*");
    std::smatch match;

    if (std::regex_match(s.begin(), s.end(), rgx))
        std::cout << "regex_match: match\n";
    else
        std::cout << "regex_match: no match\n";

    if (std::regex_search(s.begin(), s.end(), match, rgx))
        std::cout << "regex_search: match\n";
    else
        std::cout << "regex_search: no match\n";
}

Output:

regex_match: match
regex_search: no match

Is my assumption that both should match wrong, or might there a problem with the library in GCC 4.7.1?