【Busy】 , 【industrious】 , 【diligent】 , 【assiduous】 , 【sedulous】 mean actively engaged or occupied in work or in accomplishing a purpose or intention.

【Busy】 may imply nothing more than that the person or thing referred to is not idle, that is, that he is at work or that it is in use.

In attributive use and some predicative use 【busy】 usually implies habitual or temporary engrossment in activity or the appearance of such engrossment.

【Industrious】 applies to one who is characteristically attentive to his business, work, or avocation; it implies habitual or continual earnest application.

【Diligent】 may stress care, constancy, attendveness, and thoroughness, but it often implies application of these to some specific object or pursuit; thus, one may be 【diligent】 in seeking some favorite end without being in general 【industrious】 .

【Assiduous】 implies studied and unremitting, and  【sedulous】 , painstaking and persevering application to a business or enterprise.