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.