How were the ideas of the Puritans different from those of the Separatists?

The Puritans had the idea that the English Reformation retained too much Catholic influence, Puritans wanted the Church of England to further separate from the Catholic religion and follow stronger beliefs. Separatists believed that the Church of England was too much like the Roman Catholic Church; but Separatists wanted nothing with the Church of England. Puritans and Separatists believed the Church of England needed reform, however the Separatists did not want to stay with the church till it changed.