Inspection as in school administration has a negative connotation in the sense that it is more likely to be a a fault -finding attitude....whereas supervision is more positive and constructive as it deals with improving the educational system by providing leadership, motivation and leadership to the school teachers with a view to improving their teaching methodology.
Inspection is looking closely at something or someone, usually to detect faults or problems, with a view to giving it/ them an assessment of some kind. For example, suspect goods going through customs are inspected by the customs officers - the officers look all over/ through the goods to see if anything is wrong with them. If nothing is wrong they are passed as "in order" or a similar term , indicating that the inspection has been carried out and everything is OK. Basically this is what all inspectors do, whether they are looking at food safety, school standards or whatever.
Supervision, on the other hand, really means "looking from above." If you supervise someone/ something, you keep a general eye on their activities and usually help to direct them. As an employee, if you work under supervision, it means that your line manager tells you what to do, and is usually around to check that you are working well; but if your work is inspected, it means that s/he takes what you've done and examines it very closely, looking for faults.
