I hear you wideawake, it like the Tea Party and the Democrats being the exact same thing because both claim to be Americans.
Not exactly.
Unlike Democrats and Tea Party members, the Nonconformist Puritans and the Conformist Puritans had the same beliefs and values, they differed only in tactics.
The Conforming Puritans decided that they could transform the Church of England from within, while the Nonconforming Puritans thought that this was too difficult.
The Civil War made these tactical disagreements moot.
In any case, to an Anglican like Richard Hooker or William Laud, Robert Browne and William Brewster were both Puritans and their tactical disagreement with one another did nothing to efface the similarity of their theological beliefs.