A contact lenses fitting is more expensive than a standard vision examination for glasses. There are several reasons.
The doctor (Optometrist or Ophthalmologist) must measure more perimeters of the eye than for glasses. And, they need to determine a material that performs well for the patient. Both soft contacts and hard contacts come in wide variety of materials, not just different brand names. Different patients do better with different materials for a variety of reasons.
The doctor's office must supply training on the proper care of the contact lenses prescribed. Different contact lenses materials require different solutions and disinfection techniques. And, different patients will receive different wearing schedules. Some may be scheduled daily wear, others extended wear. And still others may be scheduled for continuous wear.
The doctor includes a follow-up visit(s) until the fit is a success.
The doctor's office guarantees satisfaction with the contact lenses, and may need to switch the contact lenses material, or supply a refund for the extra cost if the patient is not successfully fit.
All of these extra fitting costs are figured into the "contact lens fitting" fee.