This is a very good question and, in one sense, the answer is, "There is no difference." In another sense, the answer is, "Two are different types of the third." Let me explain.
Originally, there was one Christian Church and that was what is called the Catholic Church. Then, beginning with the establishment of Constantinople as a second government seat for Roman Emperor Constantine and ending with the Schism of Antioch (330-415), there came to be two branches of the Catholic Church. These were the Latin (speaking) Roman Catholic Church and the Greek (speaking) Constantinople Orthodox Church. Protestantism arose as the third form of Christianity when Martin Luther began a debate in 1520 about the Biblical grounds for Catholic practices. Protestants are those who adhere to what Luther taught.
Now we have sorted out Protestantism: it was a reaction against what Luther saw as a corrupted Roman Catholic Church (Luther didn't directly address the Orthodox Church since he had no significant direct contact with it). This first form of Protestantism came in time to be called Lutheranism after Luther himself.
Puritanism and Presbyterianism are two other forms of Protestantism that sought to reform the practices of the Catholic and/or Anglican Church. Both arose at about the same time, which was twenty to thirty years after Luther's first protests. Puritans adhere to Puritanism. Presbyterians adhere to Presbyterianism.
Presbyterianism was developed by John Calvin in Geneva, Switzerland, where his Ecclesiastical Ordinances were enacted by the town council in 1541. Calvin's Ordinances outlined a Biblical order of church governance that comprises part of Presbyterian Protestantism.
Puritanism arose in England about a decade later during the reign of Queen Mary (1553-1558), a Catholic, and sought a simplification of church ritual and formalism in worship and a greater emphasis on personal reading of the Bible.
Now it is more clearly seen that Puritanism and Presbyterianism are different from each other because they are both forms of Protestantism that developed in different places, though at about roughly the same time, as a result of Luther's protests against the practices of the Catholic Church. It is now clear that neither Presbyterianism nor Puritanism is different from Protestantism because both are forms of Protestantism and both sought reforms to Christianity as it was practiced in the 1500s in Europe.