Barge boards are arguably a specific type of fascia on the gable end of a building (with the triangle shaped section of external wall meeting the roof).
While fascias are roughly parallel to the ground and face outwards from the roof (positioned vertically - i.e. perpendicular to the ground), barge boards specifically refer to those that run from the bottom of the roof up along a slope to a peaked roof.
Like fasicas, barge boards also have soffits underneath, combining to protect the home and cavity under the roof from the weather and help to keep excess moisture out.
