I tend to call the games I enjoy as Euro Games. Whilst I appreciate that the origins of games are no longer purely european, the style and nature of these games definitely have evolved from the classic euro games, and have origins from UK, France and most predominantly Germany.
Although, your question is quite broad. Whilst the games I play are certainly in the Euro Game category, this site is for all board games, including the likes of monopoly, cluedo, pictionary and other younger audience games, but they certainly fall within the remit of this site. So I don't think you can categorise the whole site in any way other than saying Boardgames.
Boardgames to most people means Monopoly-esq games. But we know better in that it is the top of the taxonomy tree.
EuroGames/German Style/Modern boardgames means puerto rico / power grid style games, and is a subset of boardgames, and the ones most discussed in this site.