"In the key," in America, usually means the circle surrounding the free-throw line, and most typically, the top of that key being nearest to center court. The lane (or paint) is only the rectangle below the free-throw line and under the basket. The key and the paint share only one-half a circle (the half below the free-throw line).

However, in American usage (at least I've never heard otherwise, and I am a 7-times-a-week basketball player) the key is usually an abbreviation of "the top of the key" and only means the area closest the center court where the three point line and the free-throw circle intersect.