APQP = Advanced Product Quality Planning
APQP is the entire quality planning process from designing a concept through PPAP (see below). This typically includes, but is not limited to, Design/Process FMEAs, Measurement System Analysis, capability studies, Control Plans and PPAP.
PPAP = Product Part Approval Process
PPAP is the approval process for the product. It includes the major elements of APQP listed above, plus dimensional, material and performance verifications.
Note: this is far from inclusive. AIAG publishes manuals for each of the topics listed above.