The black tiles were used in higher temperature areas.
High-temperature tiles used a black borosilicate glass coating and
covered areas of the vehicle in which temperatures reached up to
2,300F. Low-temperature tiles contained a white coating with the
proper optical properties needed in areas of the vehicle where
temperatures reached up to 1,200F.
Reference: Gary Milgrom. "Space Shuttle Thermal Protection System" (quoted here)
I have no specific knowledge of why one area would change from black to white, but the tile / blanket layouts on the Orbiters did change from time to time. I could speculate that if a white tile showed heat damage, or someone "sharpened their pencil" and did analysis to show that a border area might experience higher temperatures than previously thought, they might replace it with a black tile.
The Space Shuttle Press Reference Manual lists the following tile & blanket changes made to the Orbiters after the Challenger accident:
The area aft of the reinforced carbon-carbon nose cap to the nose
landing gear doors has sustained damage (tile slumping) during flight
operations from impact during ascent and overheating during re-entry.
This area, which previously was covered with high-temperature reusable
surface insulation tiles, will now be covered with reinforced
The low-temperature thermal protection system tiles on Columbia's
midbody, payload bay doors and vertical tail were replaced with
advanced flexible reusable surface insulation blankets.
Because of evidence of plasma flow on the lower wing trailing edge and
elevon landing edge tiles (wing/elevon cove) at the outboard elevon
tip and inboard elevon, the low-temperature tiles are being replaced
with fibrous refractory composite insulation (FRCI-12) and
high-temperature (HRSI-22) tiles along with gap fillers on Discovery
and Atlantis. On Columbia only gap fillers are installed in this area.
(in this quote, HRSI-22 refers to the black tiles and FRCI-12 refers to the white tiles).
I scanned this picture from my 1982 hardcopy of the press manual to show the original layout of the tile types and blankets.