"Downing" comes from A. J. Downing, the guy who probably did the most to popularized the Gothic Revival style for residential architecture in the mid-1800s. He wrote a few books, among them, "The Architecture of Country Houses", which got carried all over the country by builders -- sort of an early how-to house plans book. If I remember correctly, he was actually a landscape architect who was interested in buildings blending into the land - sort of a naturalistic approach - in contrast to the then-dominant Greek Revival. I think Carpenter Gothic is a relatively recent term adopted by architectural historians to describe the homes and churches built in the style by your average carpenter. The carpenters were translating a style that been, historically, of masonry construction, into wood.
Getting a hold of Downing's books is a good start. You've probably already been through back issues of Old House Journal in the library.