Vassal in chief, or the more common term Tenant in Chief, denotes the high nobles who held their lands directly from the King (as opposed to holding them another nobleman or churchman). Such men were the backbone of the King's influence throughout the realm and include Princes and Dukes (most of whom were immediate relatives of the King), and Earls (the title Earl being an English term for Count).
In any case, the term Tenant in Chief would have been alien to the people of the time--the Magna Carta, for example, addresses the "Archbishops, Bishops, Abbots, Earls and Greater Barons." No mention of Tenants in Chief. The term is actually a construction of later historians.