A single-ply membrane performs the waterproofing with a single sheet of material. The material is either rubber-based (EPDM) or plastic-based (TPO or PVC). The material comes in varying thicknesses – .040″ thick to .090″ thick. EPDM is usually black but can come in white (much more expensive). EPDM can come with a fabric mesh embedded in the rubber (called reinforced) or not. EPDM rolls are joined together with seam tape (double-sided tape) within the last 15 years and prior to that adhesive. TPO and PVC are plastic based but chemically different from each other. Both TPO and PVC always have the mesh fabric embedded to provide strength. TPO and PVC usually come in white, gray and tan (sometimes other colors). TPO and PVC seams are heat welded with hot air. The advantage of a single-ply waterproofing layer is cost and flexibility. It also comes in wide sheets which require less seams and is easier to flash around penetrations (less chance of applicator error). The disadvantage is that it can be punctured more easily than modified bitumen or built-up roofing waterproofing layers. If you want a white roof then choose TPO or PVC. If you are comparing prices of EPDM to TPO/PVC, then to compare it properly the EPDM should be reinforced EPDM.
PVC is generally the most expensive, followed by TPO, reinforced EPDM, then non-reinforced EPDM. The thicker the membrane the higher the cost