A higher position is simply a position that is valued more highly than another, and need not necessarily be a senior position. For example, in an office a filing clerk might be higher than a messenger (I don't if they still have those in offices!), but they are still both junior positions. A senior position would be one which carries a degree of responsibility - for example a manager or a director etc.

A senior position means a position of authority in a company. A higher position is comparative - you have to know 'higher than what'? Higher than your position at the moment, maybe?