بدون
means 'without' as previously mentioned .
عدم
is negating the succeeding noun in the sense of 'non' , 'no' or 'don't '.
It is the contray of 'existent' ,it means then 'nonexistentence' or 'the lack of'.
It bears all those meanings and the context and sentence determines which word will be used precisely for each context .
Examples:
- أرجو عدم الإزعاج
- Please, don't disturb.
- المشكلة تكمن في عدم وجود موارد بشرية كافية
- The problem lies in the lack of sufficient human resources.
- عدم وجود تنظيم علي المستوي الإداري أثر علي أداء الشركة
- The lack of organization at a managerial level effected the performance of the company.