Jean Bodin said in his Six Books of the Commonwealth:
The fourth is the simple vassal who owes faith and service for his fief, but is neither a sovereign himself, nor the natural subject of the man of whom he holds the fief. The fifth is the liege-vassal of a sovereign prince but not his subject.
The liege-vassal owes obedience to his lord in relation to and against all. The simple vassal reserves the rights of his lord's superior.
But I didn't understand Bodin's explanation of the difference between these two types of vassals.