"My ..." is for files intended for the user to access directly. For instance photo apps will naturally save their photos in "My Photos", but just the photos, and with the understanding that the user can reorganize them, open them with other apps, etc... Apps that put their crap in "My Documents" are likely not following the best practices.
Note that not all folders in %userprofile% are called "My ...". For example "Downloads" (you are not supposed to modify stuff there, just read and delete) or "Desktop" (you are not supposed to access it through the explorer). The OS won't stop you, but the fact they aren't "My..." is a hint that it is not their purpose.
Linux has one single standard, all that software doing random stuff is non-standard.
And the standard says it's configurable, so I don't know what of your examples is the correct one on your machine.
> A number of efforts have been made in the past to standardize the layout of home directories, including the XDG Base Directories specification [9] and the GLib conventions on user directory contents. [10] Additional efforts in this direction are possible in the future. To accomodate software which makes use of these specifications and conventions, distributions may create directory hierarchies which follow the specifications and conventions. Those directory hierarchies may be located underneath home directories.
So one standard saying you should look at other standards. XDG from freedesktop.org is the most popular (and probably the one you are referring to). However, it relate to Linux desktops, it says nothing about non-desktop applications (ex: bash, ssh, git, ...). About git, it would a bit ironic for git, made by Linus himself for working on the Linux kernel to not follow the "one standard".