These adjectives all refer to activity or involvement. Busy is the least formal word. It may indicate nothing more than that a person is working on or doing something or that a thing is in use.

• Mr. Brown is busy right now; The line is busy .

Or it may imply constant, concentrated involvement in business or intensive and varied activity of any kind: a busy man; a busy day; a busy market place; a busy legislative session. The effort involved in being or staying busy may be, by implication, valuable or productive: Get busy and get something done. But in some cases, the word gives a special overtone of empty fuss and hollow results: busy work to keep the troops out of trouble; kept busy half the day by peddling neighbourhood gossip.

Active stresses action, operation or involvement as opposed to passivity or dormancy: an active man; an active life; an active listing. Active accounts are productive and active investments yield interest. An active volcano is not extinct but may erupt, though it seldom does. Used of persons, active often points to actual work or participation as contrasted with mere approval or association: active on behalf of the spastic centre; active in community affairs; an active club members as opposed to a mere name on the rolls. A soldier on active duty is involved in military service on a full-time basis, but he may not be busy all the time. Active may also mean brisk or lively, suggesting a heaviness of traffic or transactions: a day of active trading.

Occupied shares with busy and active a simple contrast with idle. When used of a person, it suggests his involvement with a specific task: occupied with sweeping out the fireplace. When used of an object, it suggests it physical use at that moment. A telephone line can be busy but cannot be occupied . Conversely, a telephone booth can be occupied but cannot be busy. Occupied , when used of someone’s mental state, means absorbed in thought, either purposive or idle: occupied in adding the figures before him; She occupies herself with trifles. In either case, it can suggest concentration to the point of distraction: so occupied in thought that he did not see the speeding car. Engrossed compares closely with this special use of occupied , implying even greater concentration, but with the added suggestion of pleasurable, willing or fascinated involvement: engrossed in a good mystery story; engrossed in his work.

Engaged suggests involvement, like busy , but implies concentration on a specific task, like occupied . It also has a special sense of coming to grips with a situation: The engaged artist struggles to state the dilemmas facing his society. It has a military use for units involved in a hostile encounter: The engaged patrol was cut off from its own front line. It also refers to a man and woman in the formalized period of courtship just before marriage: an engaged couple.