It's like the difference between bitch and cunt, pretty interchangeable.

Hambeast and landwhale are saved for those who are obese or morbidly obese. Though landwhale is more fitting for the later. Fatty-chan is for those who are overweight, but not yet obese. Like they might still be cute in a fat way.

How insecure you are with your body image and how much you dislike the person you're referring to.

A fatty-chan usually has a nicer attitude, though is still overweight.

A hambeast is obese. The term is usually used for ones that acknowledge they're fat, but do nothing.

A landwhale is usually a stuck-up or delusional bitch who thinks she's entitled to special treatment for some reason. Typically, landwhales are completely unaware or do not acknowledge their status as a stain upon humanity.

It's all about attitude vs. weight.

A fatty-chan is your standard overweight weeb. Not too obnoxious, not morbidly obese.

A landwhale is fatter, but the same amount of obnoxious.

A hambeast is as fat as a landwhale, but ten times more obnoxious.

Fatty-chan, general fat chick
Hambeast, annoying fat or obese cunt with poor social skills and occasionally poor hygiene, usually the subject of "con horror stories"
Landwhale, morbidly obese chick

Someone correct me if I'm wrong.

Hambeasts are the least liked.