Let's say you have input data x and you want to classify the data into labels y. A generative model learns the joint probability distribution p(x,y) and a discriminative model learns the conditional probability distribution p(y|x) - which you should read as "the probability of y given x".
regarding the first question,
the tracker searches for similar features that represents the object. could be color, texture appearance, shape and tries to formulate an appearance model that best fit the object. then at each time it is going to search for that object, it is going to use this model to find the best match.