1) Lambskins with the wool dressed outwards, a common word in early records.
1314 pro j furura de bugeto, Bolton Priory
1456-7 In xxv pellibus de Budge pro d’no Abbate iijs, Fountains Abbey
1562 One gowne ... garded with velvet and furred with budge, Thrintoft. The fur could be black: 1518 a gowne of russet furred with black bugge, London and Halifax. According to Veale the skins were imported originally from the small kingdom of Bougie in North Africa [peaulx de Bougie] and the term later came to include lambskins from other Mediterranean sources. The OED considers the origin to be obscure but suggests a connection with Old French bouchet or buchet, meaning kid, and certain references support that possibility: 1313-4 Pro j furura de bucheto ad opus eiusdem iiijs, Bolton Priory.