As a man and a writer, the only thing more difficult than describing women's fashion is describing men's. This is because I, like most men, simply do not give a damn about fashion.
I own three kinds of shirts, and I describe them categorically, not specifically. This does not cut it in description, so I've had to do more than a little research on men's clothing over the years. Treat this as a quick primer on what I've learned about shirts.
Tee-shirt. T-shirt. Neither of these is, from what I can tell, more or less correct than the other. I also believe these are the default setting for the word "shirt" in the 21st century. If you are not more specific than that, this is what people are going to imagine. This is important because a t-shirt is a very casual bit of attire, and dressing a character up is going to be difficult once the reader has imagined this.
Button-down. Did you know there's nothing formal about a button-down shirt? Did you know that a button-down shirt is not a shirt with buttons going all the way down the front? Well, me neither. A button-down shirt is a shirt with buttons holding the collar down, ostensibly so they don't get messed up while you're playing polo. Fuck me, right? These may be plaid or checkered or striped or whatever.
Polo. Oddly enough, these almost never have button-down collars. Also called a golf shirt. It's that crappy thing with a collar that only looks right once, has two or three buttons, one or two of which are never used, and which is usually impossible to tuck in.
Hawaiian. Floral print. Worn by Magnum P.I. and other real men. Only real men need apply. Warning: floral prints may include scantily clad women.
Work shirt. I don't know how universal this is, but to me this describes the kind of blue, long-sleeved shirt we associate with "blue collar" employment. Usually owned by a uniform company and rented by a man who busts ass for a living.
Button-up. Button-front. A shirt with buttons all the way down the front. Yes, these may or may not have button-down collars. Jesus I hate fashion. Usually not plaid or checkered or striped or whatever.
Dress shirt. I don't know any other way to describe this. I'll let you know if I ever need to write James Bond. Who the hell do you think you're talking to? My name is "John," not "Ian."