A buttoned down shirt has a collar that can be secured with buttons.

Buttoned down shirt tends to get used as a more generic description for many business style / corporate / traditional shirts.

A blouse is a loose fitting shirt.  However its more frequent generic use is a womens dress shirt or top.

Based on where I think people would search, I tend to use shirt if it is corporate wear and buttons up in some fashion, and blouse for most other things. 

lol though if a top is loose fitting I tend to use tunic.  choices, choices, choices