Is this project for descendants of EVERY Phelps family with roots in northeastern North Carolina?

No.  In the 1600s, Nicholas and Hannah Phelps had two children, Hannah and Jonathan.  They were in New England.  When Nicholas died, Hannah married her widowed brother-in-law, Henry.  Being Quakers, they migrated to North Carolina to escape religious persecution.  If you descend from Jonathan, then you would want to join a Phelps project for New England.  If you descend from the daughter, Hannah, then you might also wish to join a Phelps project for New England, but some of her descendants remained in northeastern North Carolina and intermarried with different Phelps families in northeastern North Carolina.

What do you mean by northeastern North Carolina?

In this case, it refers to the modern day counties of Bertie, Camden, Chowan, Currituck, Dare, Gates, Hertford, Hyde, Northampton, Pasquotank, Perquimans, Tyrrell, and Washington.  The Phelps families found in those areas so far have been the one of Henry and Hannah Phelps (her children were with her first husband, Nicholas Phelps, and the family came from New England), those who descend from James Phelps who died in Gates  County in the late 1700s (his descendants moved down into Bertie County), and the Phelps families of Tyrrell and Washington counties, as well as those who descend from Moses and James Phelps, who were mentioned as sons in the will of a James Felps of Chowan County in the 1700s - YDNA testing so far identifies the descendants of these men as being genetically related to the men with Tyrrell and Washington roots.

What makes this project different from the Phelps YDNA Surname Project?

That project only accepts YDNA testing, and is for Phelps all over the world.  This project, being geographical in nature, accepts the three types of DNA testing offered by FTDNA: at-DNA, mt-DNA, and YDNA.  If you are a male Phelps who has done YDNA testing, and you're not a member of the Phelps YDNA Surname Project, then you are encouraged to do so (even if your current surname isn't Phelps).