Primary Key is a combination of unique and not null. It can be a collection of key values called as composite primary key. Partition Key is a just a part of Primary Key. There are several methods of partition like Hash, DB2, Random etc..While using Hash partition we specify the Partition Key.
Primary key is the key we define on the table column or set of columns(composite pk) to make sure all the rows in a table are unique.Partition key is the key that we use while partition the table(in database), process the source records in ETL(in the etl tools). We should define the partition based on the stages( in datastage) or transformations(in Informationca) we use in the job(Datastage) or mapping(in Informatica).To improve the target load process, we use partition.If u need more info, plz go through Database doc or Datastage or Informatica doc on partitioning