Nymphs are minor nature gods who are generally associated with the environment which they take care off. Their names change depending on what domain they are taking care of but their are six main types: celestial/sky nymphs, land nymphs, wood nymphs, water nymphs, underworld nymphs and cultural nymphs (aka Muses).
Dryads are the children of Persephone, and a specific type of wood and plant nymphs. Although in Greek mythology dryads were responsible for oak trees, they are actually assigned a specific tree (no matter its species), and they can always distinguish them from others, and will be able to find them no matter where they are.
Among other powers, they can communicate with wood, even ship's wood, like Julia did during the Muntjac's voyage to the end of the world, and time travel, as Julia does it to teach young Jane Chatwin how to make a clock tree.
Physically, in the book, they are not much different from their human selves except taller and more God-like, with a beauty surpassing any human being. In the show however, their skin and possibly body are infused with shrubs, herbs and pieces of wood.
Naiads are responsible for fresh bodies of water in Greek Mythology. In The Magicians book, a naiad appears in a river making her a Potamide.
This naiad had gills in her neck, webbed fingers like ducks and pointed teeth like a shark. She told Quentin that his group should not be in the war happening in Fillory, and gave him a blowing horn that turned out to summon The Beast.
"Be sure to distinguish between naiads and dryads, species of nymphs that take great offense at being mistaken for one another. Naiads are seductive water spirits you'll need to appease in order to cross certain rivers, but watch out - they bore quickly, and what naiads don't have use for, they drown." - Welcome to Fillory
"Dryads, on the other hand, are aloof arboreal spirits who live amongst Fillory's sentient trees. If you ever win them over, dryads can help you navigate Fillory's more obstinate woodlands." - Welcome to Fillory