The shoulder pips = ENT rank pips (which are simplified compared to TNG ones, with no half-pips). Sleeve stripes = TOS sleeve stripes. At least, that was my impression.
I noticed that Kirk wore a unique badge on his dress uniform - one identical to the one Admiral Kirk wore in The Motion Picture. The Admirals had a similar-but-different version (gold and stylized), and everyone else wore plain silver arrowheads.
Perhaps the uniform, badge and pips combine to give an extremely detailed account of one's rank and service history, if examined closely enough