Conventional reservoirs are those reservoirs such as sandstones and limestones with reasonable porosity and permeability. Typical old wells of Oklahoma with vertical wells with some directional or horizontal wells.
Unconventional reservoirs are formations such as shales with low porosity and permeability that cannot produce without special completion techniques such as high pressure and proppant frac’ing. Examples are the Woodford, Hunton, Mississippian Shales, Goddard Shales.
I can get you an exact definition, but is that close enough for now?