Genetic only in shape, consistency, thickness and smoothness of the enamel of her teeth (could be congenital as well), and the output of saliva. All the bacteria in your dog's (and yours as well) is acquired. The first inoculation of bacteria is from the mother and is introduced via the birth canal, the mother licking the pup, and any other foreign bacteria in the pups immediate surroundings and on the mothers body/nipples. Bacteria continues to be introduced throughout the pups lifetime as it shares toys, training aids, water and food dishes, other dogs' mouths, and even from their owners. A typical bacterial load for a dog is around 140 different types of bacteria (humans have over 700!) of those, only 12 or so types cause problems with decay or periodontal disease.
Now that doesn't seem to matter because you have an issue with plaque, right? Well, consider what plaque is made of: dead and sloughing skin cells (all that pink or other colored tissue is skin!), dead and dying bacteria, bacteria that eats and breeds in those "food" sources, food and other debris, and minerals, salts, calcium,etc from the saliva. If your dog produces only a slight amount of thick and ropey saliva, all of that "stuff" will stick to every surface and not be washed away like it is with copious thin saliva drooling dogs.
Think about your last dental visit and cleaning. Just how long did that "slick" clean feeling last? I'll bet you were running your tongue around checking out all the smooth feeling surfaces! And in doing so, you were re-coating the teeth with a bacteria laden matrix called the "pellicle" which is essential in keeping your teeth from drying out, holds good bacteria close against the teeth, and keeps your teeth insulated against sudden temp changes.
Since you probably didn't brush your dog's teeth twice a day as well as flossing, your dog tends to build up plaque and staining fairly quickly. As far as why one gets it faster than the other, could be any of the above listed things, just like one person gets plaque buildup every 3 months and others can go for many years without ever getting plaque/tartar buildup.