Knights bachelor are household knights, who live with a lord and are kept by him with salaries in cash or kind. They are the body guards and elite warriors of their lord, and should be unflinchingly loyal to him.
Knights errant, like knights mercenary, have been knighted by a lord, but have sworn no oath of alliegance; Instead they roam the country in search of honourable quests and glory. Usually, being a knight errant is an euphemistic way of saying that one has no steady employment, and perhaps no interest in getting one. Some knights errant are simply idly rich, others are brigands, professional duelists, or try to make their living from tournaments.
Knights mercenary, like knights errant, have been knighted by a lord, but have sworn no oath of alliegance. Instead, they earn their keep by working as soldiers or mercenaries.
A knight vassal has been granted a manor (or more) in fief from a liege. They manage their own affairs, and keep their own manor house. They are obliged to serve a fixed period in the field for their liege every year (usually 40 days), and thrice as long in garrison duty. They are also obliged to bring some men-at-arms (the number and equipment vary with the fief). The liege may ask for an extension of the serving period by 50% without offering compensation. Intead of serving as a warrior, a vassal may pay scutage. A vassal is also obliged to attend the court of his liege, and to offer advice when his liege requests it.
Lords are knights of banneret or peer rank. They command other knights, and have large holdings, most of which are held in fief from a liege (the king or a greater peer), some of which may be owned. A lord will almost invariably be served by knights bachelor and vassal.