Shaun of the Dead (2004) is an interesting comedy with aspects of grief, stagnation, and acceptance, while also being full of zombies, and has introduced me to the term shambolic, a British term meaning chaotic, disorganized, or mismanaged, which is my new favorite adjective to describe that sort of zombie.
While shows like The Walking Dead will try to provide a realistic idea of human rationale in a zombie apocalypse, Shaun of the Dead goes for the exact sort of ideas one might develop should they play an incredibly intricate zombie VR game, crafting loose, fun plans, and holing up in a bar.
Shaun of the Dead goes for a very reserved zombie design, leaving the skin to be naturally colored, and only darkening slightly with time. Becoming a zombie limits movement speed to a staggering trudge, and while they can be a startling mass, individually they seem quite easily dealt with.
These zombies are stupid. They have no organization, are weak, and move slowly. They seem to be only able to infect through a bite, and while they become mostly mindless, they can be interacted with in slight ways when attempting to contact the old personality. They hunt through detecting a visual distinctness in humans, meaning groaning and trudging as they do will effectively camouflage you. A very week shambolic zombie.
The transformation as noted above is very limited, only changing the eye color of the victim.
They are simply called zombies in the film.
Watching Shaun of the Dead (2004)