There is vegetable rennet, which is made from enzymes found in safflower, melon, fig leaves or thistles, and there is microbial rennet, which is made from mold cultures or bacteria or are created artificially in a lab.
While vegetarians who made the lifestyle choice because of animal cruelty try their best to avoid cheese rennet, vegan individuals usually avoid cheese altogether, since it is made with dairy products.
Unfortunately, manufacturers are not required to name the source of their rennet on the package labels, so it's safest to find a cheese that is certified safe for vegetarians or vegans.
Animal rennet is one of the most common ingredients in mass produced cheese, which can make it quite a hurdle for those looking to only eat cheese with vegan rennet.
The words vegetable enzymes are a guarantee that the rennet is vegan, but enzymes is generic enough term that it can refer to both animal and vegan sources.
More specifically, they digest the sugars in the milk and produce lactic acid, which makes the milk curdle and solidify, just like animal rennet does.
ABOMASUM (caillette), the fourth or rennet stomach of Ruminantia.
Another enzyme, rennet, which in the animal body is proteolytic, is frequently met with in plants, but its function has not been ascertained.
By the rennet ferment caseinogen is converted into casein, a substance resembling caseinogen in being soluble in water, but differing in having an insoluble calcium salt.
Thus the digestive function, in its largest sense, is now seen to consist, not only in preparation and supply, but in no small measure also of protective and antidotal conversions of the matters submitted to it; coincidently with agents of digestion proper are found in the circuit of normal digestion "anti-substances" which neutralize or convert peptones in their poisonous phases; an autochthonous ferment, such as rennet for instance, calling forth an anti-rennet, and so on.