What is the difference between deep hyaluronic acid filler and surface one?

The answer depends on what you are having treated. Certain fillers are placed deep to add structural support to the soft tissues such as when Sculptra Aesthetic or Restylane Lyft are injected into the midface/cheeks while other fillers are placed more superficially such as Restylane Defyne when treating laugh lines or Restylane Silk when treating lip lines. 

Years ago when fillers first hit the market, they were more commonly called dermal fillers, as the treatment goal was to typically address more superficial lines (wrinkles), with varying success. As the understanding of how the face ages and development of better fillers and injection techniques, the concept of injecting deep, to replace bone and refill the deep fat pockets of the face evolved. 
Without a consultation, it’s difficult to say which treatment is best for you. But typically, the idea of “restoring the foundation”, is preferable to than just “fixing the siding”. 
Whatever path you choose, make sure you have an doctor who understand these differences and does not try to overfill, but takes a gradual approach to facial contouring, allowing the tissues to adequately accommodate each treatment, before adding more.