I was introduced into "Euro" games about 8 years ago when most games in that genre did originate in Europe. Since then, it has become a blanket term that more or less covers games that are not made by Hasbro, Parker Brothers, etc (although they do have some enjoyable games), or are not found on shelves at the big box stores. Ameritrash to me has been a term for the games that are either almost solely based on luck (Sorry!) or just require a lot of Die rolling (lucky rolls) like Monopoly. There are plenty of strategy, engine building games that don't come from the Euro market.
I think the gaming industry has evolved a bit into more categories, such as; Mini's, Worker Placement, Engine Building, 4x, Party Game, Deck Builder, Set Collection, Drafting, etc, and some of the best games out there use mechanics found in several genres. There are plenty of Euro games that use dice, and chance, but also have a lot more decision making than most mainstream games. Most of the games in the "Euro" or "Strategy" game genre are not as mainstream due to the fact that the smaller companies tend to not be able to get shelf space at mainstream stores like Target, Walmart, etc. and are found in stores that a majority of people won't walk into.
As I understand it, "Ameritrash" originated as a term for mass-market games in the pre-BGG internet, and eventually mutated to mean "thematic games" instead (encompassing Cosmic Encounter, Fortress America, etc - an entirely different definition from the original)
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I think the gaming industry has evolved a bit into more categories, such as; Mini's, Worker Placement, Engine Building, 4x, Party Game, Deck Builder, Set Collection, Drafting, etc, and some of the best games out there use mechanics found in several genres. There are plenty of Euro games that use dice, and chance, but also have a lot more decision making than most mainstream games. Most of the games in the "Euro" or "Strategy" game genre are not as mainstream due to the fact that the smaller companies tend to not be able to get shelf space at mainstream stores like Target, Walmart, etc. and are found in stores that a majority of people won't walk into.
Source: http://boardgamegeek.com/wiki/page/Ameritrash#toc14