There are two main ways to represent a string:
A sequence of characters with an ASCII null (nul) character, 0, at the end. You can tell how long it is by searching for the terminator. This is called a null-terminated string, or sometimes nul-terminated.
A sequence of characters, plus a separate field (either an integer length, or a pointer to the end of the string), to tell you how long it is. I'm not sure whether this is ever called a "usual string". What quite often happens is that when talking about a particular language, the word "string" is used to mean the standard representation for that language. So in Java, java.lang.String is a type 2 string, so that's what "string" means. In C, "string" probably means a type 1 string. The standard is quite verbose in order to be precise, but people always want to leave out what's "obvious".
I'm not sure about "usual string", but what quite often happens is that when talking about a particular language, the word "string" is used to mean the standard representation for that language. So in Java, java.lang.String is a type 2 string, so that's what "string" means. In C, "string" probably means a type 1 string. The standard is quite verbose in order to be precise, but people always want to leave out what's "obvious".
In C++, unfortunately, both types are standard. std::string is a type 2 string[*], but standard library functions inherited from C operate on type 1 strings.
[*] Actually, std::string is often implemented as an array of characters, with a separate length field and a nul terminator. That's so that the c_str() function can be implemented without ever needing to copy or re-allocate the string data. I can't remember off-hand whether it's legal to implement std::string without storing a length field: the question is what complexity guarantees are required by the standard. For containers in general size() is recommended to be O(1), but isn't actually required to be. So even if it is legal, an implementation of std::string that just uses nul-terminators would be surprising.