Beardruff is normally used as a misnomer — meant to signify flaking from the facial skin similar to how dandruff flakes from the scalp. Beardruff is not normally the same thing as dandruff. Rather, it's more similar to dry scalp, a different condition than dandruff.
When used correctly, beardruff is the same thing as dandruff. This, however, normally wouldn't be due to a buildup of sebum, but when using artificial additions in your beard, such as beard oils and balms. These can incite dandruff in the beard. This is rarer, however, and most men that fight through flaky skin are likely to have dry skin.