regex_match only returns true when the entire input sequence has been matched, while regex_search will succeed even if only a sub-sequence matches the regex.
Quoting from N3337,
§28.11.2/2
regex_match[re.alg.match]Effects: Determines whether there is a match between the regular expression
e, and all of the character sequence[first,last)....Returnstrueif such a match exists,falseotherwise.
The above description is for the regex_match overload that takes a pair of iterators to the sequence to be matched. The remaining overloads are defined in terms of this overload.
The corresponding regex_search overload is described as
§28.11.3/2
regex_search[re.alg.search]Effects: Determines whether there is some sub-sequence within
[first,last)that matches the regular expressione....Returnstrueif such a sequence exists,falseotherwise.
In your example, if you modify the regex to r{R"(.*?\s\d{2}\s.*)"}; both regex_match and regex_search will succeed (but the match result is not just the day, but the entire date string).
Live demo of a modified version of your example where the day is being captured and displayed by both regex_match and regex_search.