Do you have to be close (within walkable distance) to I95 or the Amtrak’s Northeast Corridor in order to be in the Northeast United States ?
Slightly different terms exist among different users (the federal Commerce Dept., for example, nowhere uses the term “Midwest”), but generally you would consider the Northeastern United States to consist of everything between the Mason-Dixon line and New England: the entire states of Maryland, Delaware, Pennsylvania, New York, New Jersey and of course the District of Columbia too.
In a very casual way (say, during a weathercast when visuals take precedence over words), “Northeastern United States” is sometimes used as a blanket term that includes includes New England, but generally New England counts as its own region (i.e., Connecticut, Massachusetts, Rhode Island, Vermont, New Hampshire, Maine; and if I left anyone out I apologize).
Each region has its own historical significance and culture. New England, speaking very generally, is older and more culturally “Anglo” than the Northeastern States to its south. Traditionally the Northeastern States have been the locus of political and economic (and a great deal of industrial) power for the whole nation. That distinction is beginning to slip somewhat given the relative shift in population toward the South and the Southwest (or “Sunbelt” if you must), but note for example how many cultural institutions (Harvard) are in New England and how many commercial institutions (NBC-Universal) are headquartered in some large Northeastern city, usually New York.
Note that the traditional term “Northeastern United States” says very little about geography or climate zones and in fact considerable portions of New York State and Pennsylvania are west of what social-science types like to call “the Appalachian Construct,” meaning they are at or beyond the point where American mountains cease to exist 'til the Rockies. It took later to settle the trans-Appalachian west, which is why Pittsburgh sometimes acts cuturally more Midweste