There are many different signals the OS sends to applications which are kinda like "Can you kill yourself?" or "Please kill yourself" or "I will kill you" to close it. In computer teminology, there is "close", "terminate" and "kill" types of signals. These are used so that applications can have time to perform closing tasks (like saving) when neceassary and if they misbehave, just "kill" it.

Now both windows and linux have these types of signals. In fact every OS has it.

I beleive this is the reason this meme exists:When the user tries to shut a app in windows (throught close button or task manager) windows will wait and not give any option to immediately kill the app. Hence some apps don't close even after using end task. Only if the app freezes for some time will it give the option for force quit, ~_{no other way}~ (edit: it exists). In linux, its the same as windows and limux waits for app to close. But the difference is that option to kill is available anytime in linux and basically gives the user full control. Although kill option in linux may be hidden as a way for users not to use it unless necassary as applications may not like it.

Shutdown process of both OS is same, they wait for all apps to shut by semding "please close" signal and if they misbehave, option to "shutdown anyways" will be shown to the user, basically killing all apps.

The meme is not correct and is just a steorotype of different OSes. This steorotype comes from how people normally experinece different OS culture and practices. Both OSes have same process of managing apps. Both OSes will wait for process to close if it freezes and give option to user to force quit. SIGKILL in the meme is coreect only for the right panel of the meme and the left panel is actually a SIGTERM (or something else which means "please close", don't remember)

The only thing the meme should emphasis is how the user is given full control to do in linux (even deleting the kernel) while windows is careful to not let users do something stupid.

Edit: Killing apps in windows can be done on demand through cmd using taskkill command