The title says it all... what's the difference? When do I use one and when do I use the other?
NTFS data files are stored with all their attributes as an "inode" with an ID, and filenames point to the inode. All files have one+ hardlink. some tools can create extra names (hardlinks) which point to the same inode, which has a counter of the number of names pointing to it. If the number goes to zero, the OS deletes the file, the inode.
Special tools, like LN can create additional filenames which point to existing inodes, using a filename that points to them. Note that all the file attributes, including dates and times are stored with the inode, not the filename.
(Extra) hardlinks are useful when you want different names to point to the same data, read or write. They save space and overhead. However, they clobber programs which assume different names point to different data. e.g, if you replace references to duplicate files by hardlinks to a single file, then you have removed any backup you have! The windows OS is one program which assumes different names point to different sets of bits.
Hardlinks have to be on the same physical and logical volume.
They are useful for:
Junction points are messier and use Reparse Points (which I do not understand). They can point to different physical or logical volumes but they have to be on the same computer. They apparently can be used like symlinks for directories, allowing a second name for the same destination, but limited to a single computer, rather than just a single volume.
Useful for reducing path lengths, or simplifying working with several programs with hardcoded directory names.
Same caveats, too! Many programs assume different names = different files.
And then there are symbolic links (which can go across networks), shortcuts and PIFs and .....
Basically, they're saying to use hard links only for files within the same volume (disk drive letter) and junction points only for directories on the same computer (they can span across different local volumes).
Symbolic link: A link to a file or directory on the same or different volume (drive letter) or even to a remote file or directory (using UNC its path).
Hard Link: A link to a file on the same volume (drive letter) only.
Junction: A link to a directory on the same or different volume (drive letter) but not to a remote directory.
Symbolic links: A symbolic link is a file-system object that points to another file system object (eg: file/directory).
Hard links: A hard link is the file system representation of a file by which more than one path references a single file.
Junctions: A junction (also called a soft link) differs from a hard link in that the storage objects it references are separate directories, and a junction can link directories located on different local volumes on the same computer. Otherwise, junctions operate identically to hard links. Junctions are implemented through reparse points.
 Hard Links and Junctions: https://msdn.microsoft.com/en-us/library/windows/desktop/aa365006%28v=vs.85%29.aspx
 Creating Symbolic Links: https://msdn.microsoft.com/en-us/library/windows/desktop/aa363878%28v=vs.85%29.aspx
Hard link is just another name for a file. If you have file named A.txt and you have link L.txt, once you delete A.txt, you will still have access to it's data through L.txt. Only when both are deleted file is gone.
On other hand, you have a so called soft-link (junction if it is folder or symbolic link if it is file). In that case, when you delete A.txt, file is really gone. Deleting L.txt has no effect on file what-so-ever.
Hard links can only be used on same partition as originating file and soft-links can be used across partitions.
P.S. File and folder are mostly interchangeable as far as NTFS goes.