Difference between the two: PMP requires 4500hrs of Project management experince that you will have to document it one project at the time and the peurcentage of your envolvement within each phase of the life cycle of each project, then you will qualify to sit for the exam ( exam I think is 200 questions and the certification is renewed every 3 years )
On the other hand CAPM is the kind a like the entry level , to meet the requirment you will have to proove that you have a 35 contact hours of PM classes or I think 1500hrs experience, its exam is 150 questions and the certification will last for a period of 5 years where you will gain more hands on Project Management which will qualify you for PMP. it is for that reason CAPM that get a re-newal or an extension.
Bottom Line since you said you are a new graduate, your best bet is CAPM, it will allow you to understand the "lingo" of PMBOK and also it will give you more profetional recognition
and will lead the way to your PMP very easily.
your brother Abdellah