The trend in taxonomy is to retain the category, but add new categories to account for more recent speciation. For example, a dog is now scientifically termed canis lupus familiaris, giving credit for its derivation from wolves, both subcategories of canis, whereas in the past the dog was termed simply canis familiaris to distinguish it from canis lupus. So today, the scientific name implies that the dog is also a wolf, and is also a canine. You can go further and include in its name (before canine) carnivore. So our dogs are dogs, but also wolves, and also canines, and also carnivore, all at the same time.
Similarly, humans are apes, monkeys, and primates, in that order, since apes derived from monkeys (a species that any zoologist would classify as a monkey - Old World type - were it currently extant), and monkeys are a category of primate. This makes a human being a human, an ape, a monkey, and a primate, all at the same time. So you can both say that we evolved from monkeys and that we remain a type of monkey, just as we remain a type of ape, and a type of primate.
