For the average user, don't worry about the difference. ;)
From the perspective of a *nix power user, people choose the desktop environment separately from the window manager. So they provide very different features. The Window Manager draws the window borders, placement, stacking, etc. The desktop environment does a bunch of other stuff, like managing the video settings, the inputs, cross-application features like cut/paste, print dialogs, and also often provides a GUI "control panel" for managing the whole OS.
Also, if you read the article, you absolutely do not need the systemd init system to use the new features. That is just another myth that the non-readers are circulating and repeating. The article goes into the specific features and what and why questions. It isn't the window manager functions that are involved, but things like the GUI login screen that comes with the desktop environment.
For example, in the old days we didn't have desktop environments. We only had window managers. So instead of being able to start Gnome or KDE from the system and receive a login screen, you'd login to your user account from the text terminal, run a script like "startx" that would have your preferred window manager and settings in it, and that would start the X Window System (which would manage the mouse/keyboard directly) and then it would start your window manager, and a few default applications that probably includes a task bar and some sort of app launcher. Copy/paste usually only worked for apps that used the basic terminal paste capabilities; apps that had more advanced cut/paste capabilities were generally incompatible with each other. And not only was their no common sort of print dialog, there wasn't even a layer in the system to hang it on. Print and copy/paste are the killer features that pushed the creation of a "desktop environment," because there needed to be a layer to attach that stuff to. It needed to be closer to the app than the X Window System, because nobody wanted to add bloat in that layer, and it needed to be closer to X than to the window manager, because people used a lot of different window managers. App developers who wanted portable copy/paste were adding support for individual window managers already, which worked poorly, so there clearly had to be another layer between that and X. Also, when you wanted a GUI login, you had to run that as a separate app to replace the startx script, which made those use cases really klunky and error-prone.
So the desktop environment is designed to run a GUI login screen as a system user, manage the related hardware configuration, allow the user to select their window manager (most gnome environments come with a bunch of different window managers) and then after it is all running, it manages the mouse and keyboard, and provides a unified cut/paste clipboard and printer dialog. It also manages lock screens, etc. Window managers have no idea if you want to lock the screen or not; they're just painting windows after all. In the old days we had background processes spying on your keyboard and mouse directly in order to decide when to launch a screensaver, and lock screens were a screensaver feature. This ties into one of the things finally getting fixed at the desktop level; using non-init parts of systemd to allow the desktop environment to monitor the user inputs, but without giving any old user process access to spy the keyboard and mouse. If that singes somebody's neckbeard it isn't going to stop me from enjoying the improved security.