Pure research is aimed to know fundamental laws in pure Sciences; for instance Einstein's formulation of the theory of General relativity was a big step in (Pure) Physics; Applied research generally uses theories formulated via Pure Research to complex domains of interest, which are related to something that can be used, for instance the technology of new materials, new ways for storing energies (batteries) both use knowledge from Physics and Chemistry. Of course also Mathematics, that is always present in whatever scientific subject has its own applied branches, for examples the studies related to the oscillations of buildings under a wave perturbation (in other words 'earthquake'), or the optimal profile of airplanes' wing or ships' prow to reduce friction. Sometimes it happens that what is today Pure Research will become in a near future Applied Research. Here is a funny (at least for me) example of the transition from Pure to Applied: The physicist Michael Faraday made in years around 1850 important discoveries in the new field of electricity; the English minister of finance, William Gladstone, asked him of the practical value of electricity; Faraday's reply was: I am not sure yet, but one day Sir, you will put a tax on it.

Pure research = research done simply to determine why something happens, i.e. what Franklin was doing with a key and a kite. Applied research = taking knowledge that we have and applying to to use, like what Edison did with the light bulb Franklin was the pure researcher, Edison used that research and applied it.