I guess the answer is already in the question. The mineral K is the pottasium mineral salts present in soil. Exchangeable K is the free pottasium in solution or loosly bound in the water film on soil aggregate. It is physically bound K, can be called soluble K. Non-exchangable pottasium is the chemically bound pottasium which is tightly bound in the crystal lattice thus, not easily available. This occurs in the dehydrated conditions. Pottasium is very soluble in soil, thus there are less chances of pottasium to be present as non-exchangable form.
K as an ion is the same whether it is in the mineral, exchangeable or non-exchangeable forms.
These terms are basically used for its ease of availability to a plant from the soil. Those fixed within the clay lattices and difficult to absorb are the non-exchangeable forms.
I agree with Abhijeet. Also, potassium availability for crops is strongly linked to the cation exchange capacity (CEC) and soil pH. You should have a pH lower than 6.5 and a CEC above 7 cmol/Kg for this nutrient to be available for the plants.
Only their relative availabilty to plant roots and solubility in the soil solution differe.Though all of these three are in state of equilibrium with each other.
Recent research clearly indicates that the K availability in soils is primarily dependent on the content of biotite mica present in soils. Crop response to to K fertilizers will depend on the biotite reserves in various soil-size fractions. A selective quantification of biotite mica in the common situation in soils containing mixtures of biotite, muscovite and K-feldspar could be an effective tool to determine the status of stock of K in soils. This information could be used to dictate the K fertilizer requirement in various soils in many parts of world and will also help in making projections for K-fertilizer production in the future. The relevant PDF is attached for reference.