Hi Lucy,
PMI is the trade association that offers the CAPM and PMP (among other) certifications. They say that:
The CAPM is designed for project team members who:
• Provide subject matter expertise (e.g. marketing, finance, customer care, processing, fulfillment)
• Serve as project team sponsors, facilitators, liaisons or coordinators
Candidates for the PMP credential:
• Perform their duties under general supervision and are responsible for all aspects of the project for the life of the project.
• Lead and direct cross-functional teams to deliver projects within the constraints of schedule, budget and resources.
• Demonstrate sufficient knowledge and experience to appropriately apply a methodology to projects that have reasonably well-defined project requirements and deliverables.
Typically, if you have the required project experience (roughly 3 yrs experience leading projects + a bachelors degree, or 5 yrs exp + a high school diploma), you take the PMP exam. If not, the CAPM is for you.
You can find the rest of the PMP requirements here.