What is the fundamental difference between psionic and psychic powers? How can a power be classified as a psionic or psychic power?
Based on the Marvel wiki entry, psychic powers are "any and all extrasensory and extraphysical powers stemming from the mind, specifically astral projection, clairvoyance, empathy, levitation, precognition, psychokinesis/telekinesis, telepathy, and teleportation." Basically, they're mind powers.
Psionic energy is a specific sort of energy that can be used to boost psychic powers.
Psions or Psionic Energy is the type of energy used by telepaths, or to mechanical means to stimulate the natural psionic powers. All the living beings produce Psions and only a few can detect this energy. The Mutant; Charles Xavier created Cerebro to enhance his already powerful telepathic abilities. The machine allowed him to monitor the entire planet and detect the specific mutant psionic signatures. Being such as the Phoenix Force and Shadow King are Psionic Entity's being made out of Psions. Psionic beings or telepaths Astral Projecting in their Astral Form can enter the Astral Plane, a dimension made of Psions.
So, in short, unless you count being able to access psionic energy as a power in and of itself, there are only psychic powers, some of which are boosted by the use of psionic energy, and creatures who are composed of said psionic energy, some of which have psychic powers.
Obligatory caveat, my source is a wiki editable by anyone, and writers have likely used the terms interchangeably.