Hey Kartik,

The answer to your question, here import export is part of international business and not the other way around. 

International management comprises of all the aspects of transactional activities such as International law,Transactional operations ,cross border setups ,ImportExport and a wide range of subjects and understandings .

Import export management on the other hand is simple handling of trade between two countries .It does need the understanding of subjects above but only of part concerning the exchange of goods.

The involvement of time and resources is quite significant when considering International businesses. 

Hope this helped!!