button-down 
adjective
1(Of a collar) having points which are buttoned to the garment.What he was getting at were such telling details as never wearing a button-down collar with a tie - I would go further on this point and revise it to the simpler, and fairer, never wear a button-down collar at all....
- It sports a slightly curious design, in that there's a button-down collar which buttons down invisibly, on the inside of the collar, by means of a tiny little loop of fabric.
- Can I wear a button-down collar with a suit and tie?
1.1(Of a shirt) having a button-down collar.The light-weight button-down shirt with banned collar and shirttail hem is designed for maximum comfort and ease of movement....
- Lunchtime brings out young-ish men in khakis and button-down shirts who avoid the homeless sleeping on benches.
- His eyes were like chips of jade gems, matching the bottle-green color of his button-down shirt worn beneath the white doctor's knee-length jacket.
1.2 (also buttoned down) North American informal (Of a person) conservative or unimaginative.That is not always an easy task in the button-down halls of Congress, where many aides remain closeted....
- Unlike most news anchors, who are known for button-down decorum and a calming presence, he has been a persistently outspoken, dramatic and frequently polarizing figure.
- At the risk of looking too button-down with the sweater set, the skirt has some little sequins on it, though you can only see the sequins if you look very closely.
noun
A shirt with a button-down collar.I tend to focus on non-dress shirts for button-downs (a cotton-poly blend, or, if you want to look good, a silk shirt), and leave them untucked....
- Luka, Nathan and Wolf are far more casually-dressed than the girls: the standardised baggy jeans, t-shirts under short-sleeved button-downs or over long-sleeved shirts.
- I tuck undershirts with polos and button-downs sometimes… regardless of whether i tuck the overshirt.