There is no separate type rating for the models to which you refer. Your average Piper and Cessna all fall under the Class Rating of Single Engine Piston (Land) (SEP(L)). Consequently, if you have trained on, say, the C172, you do not require a separate rating for the PA28. That said, it is likely that any club or school you wish to rent an aircraft from would insist on some form of training but that is a separate issue. Equally, if your are flying more complex aircraft than that on which you trained e.g. VP propeller, retractable undercarriage, turbo charged etc, you will have to carry out differences training though this does not amount to a separate type rating. I believe the only single engined piston aircraft that falls outside the SEP(L) class is the PA46 though I stand to be corrected.
JAR-FCL 1.215 (and specifically Appendix 1) refers.