It's the same medical. In fact, the ATCO one is the Class A that you need to hold a CPL/ATPL, so it is higher than for a PPL. PPL doesn't include the cardio thingie.
Sorry to burst your bubble but I have to have two medicals (done at the same time admittedly). The ATCO is still a CAA Class 1 at the moment. The PPL requires a JAR Class 2. The two different regulatory bodies, CAA and JAR, do not accept each others standards.
The physical examination may only need to carried out once but you should get two pieces of paper, one for ATCO class 1 and the other for PPL JAR Class 2.