How come the Bald Head Lighthouse was lit for the first time in 1794, but was built in 1817?

The first Bald Head Light was built in 1794 closer to the mouth of the Cape Fear River, on Bald Head Point. It had to be torn down due to shoreline erosion in 1813. The second Bald Head Light, "Old Baldy," was built further back from the shoreline, in 1817.

This physical lighthouse was built in 1817, but it is not the first one.