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The line between "monstergirl" and "furry" is generally based on the facial quality and to a lesser extent, the human-ness of the body.
Most important to an acceptable face are the browline, nose, mouth, and jawline. Barring rare exceptions such as harpies, spidergirls, and slimegirls, facial structure must appear, disregarding color, human.
Bodily anatomy is not unimportant, but is given much more flexibility than the face, due to the nature of a -MONSTER- girl. Breasts, vaginas, and anuses should be recognizable as human, but the latter two are used flexibly, especially in non-mammalian monstergirls.
Other traits ascribed near-exclusively to furries are spread shots highlighting a tail, breast fur, and non-human mammalian appendages.