I'd disagree with Mrebo's assessment of the situation. Tarkin & Co are distinctly military leaders. They refer to the Senate (the political power) as being quite separate from themselves. They have titles like "Commander" and "Admiral". They use possessive pronouns like "your" when talking about the starfleet. They are the military.

Vader, on the other hand, is a bit of an outsider. He's not subordinate to them, not even to Tarkin, but he's not exactly above them in the chain of command either. He's separate from both the political and military structures, except that it's well known that his authority comes from the Emperor. The script goes so far as to call him "right hand of the Emperor". As the films progress, particularly in ESB where he's been given use of the fleet to hunt down Luke, he has greater explicit command of the military, but he's never actually part of their system. As the Emperor's right hand man, however, he's almost always obeyed.