History

C++98 - C++14: No filesystem API

Only <fstream> to create/write files
Platform API (POSIX, Win32, ...)

Boost.Filesystem

Introduced in Boost 1.30.0 (March 2003)
Current version: 3
Compatible to C++98 or later
Base for Standatization in C++17
http://www.boost.org/doc/libs/1_66_0/libs/filesystem/doc/index.htm

Note: Version 4 might be changed to reflact C++17 std::filesstem

C++17: std::filesystem

Standatized but not widely avaiable
Header: <filesystem>
Namespace: std::filesystem
Not in GCC 7.3, but in trunk
Not in clang 5.0
Not in MSVC 19 - 2017
http://en.cppreference.com/w/cpp/filesystem

experimental/filesystem

Pre-Standard implementation of the new API
Header: <experimental/filesystem>
Namespace: std::experimental::filesystem
Available in GCC 5.3
Available in clang 5.0
Available in MSVC 19 - 2017

Differences

Mostly identical.
Various details changed between Boost.Filesystem and std::filesystem.
https://stackoverflow.com/a/46271698