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.
Soil K exists as four forms. Water soluble K is a plant available form, although its amount in soil is relatively small. Exchangeable K is widely used for evaluating the soil K status and prediction of crop K requirements. Non-exchangeable K is located between tetrahedral layers of tri- and dioctahedral micas, vermiculites, and interstratified clay . Most of the soil K is in the structure of K-bearing primary minerals (muscovite, biotite, and feldspars) and is called as mineral K. This form of K is slowly available to plants, but the availability of this form is dependent on the other K forms and the weathering nature of the micas and feldspars. All forms of K are in equilibrium and this affects the availability of K at any particular time.
What can be generally extracted off by a replacing solution like neutral NH4OAC is readily available K (water soluble K + exchangeable K). However, often such an extractable K is made synonymous with exchangeable potassium, presumably due to assumption of negligible soluble K/readily available K ratio. Meanwhile, different extractants have been used to determine readily available K (or exchangeable K) such as 0.5 M MgCl2, NH4Cl, 0.5 M MgOAc and NH4OAC which can possibly extract different amount of K.
However, the most difficulty defined and measured K pool might be non-exchangeable K as fixed K (interlayered K) and/or mineral K. Most generally it refers to K held and bound chemically (inner- sphere complex) between adjacent tetrahedral layers of phyllosilicates. Mineral K also called structural and lattice K which is native interlayer K (e.g. micas), however, non-native interlayer K (non-exchangeable K) becomes interlayered or fixed from the solution.
Whereas the soluble and exchangeable forms are regarded as being easily or readily available to plants the nonexchangeable is not. When readily available K due to plant uptake and harvesting reduces and depleted, as a result (disturbing the equilibrium) some of the nonexchangeable K may be released. The amount and rate of this release depends on the K-supplying power of soils. At very high depletion degrees, native interlayer K could be released without mineral destruction (mica weathering). Based on these distinct boundaries between soil K pools, the non-exchangeable K (interlayered) can be considered as the amount of K which is not extracted or displaced by neutral 1 M NH4OAc.