American here. My definitions, plus a few more:
Hamlet
The melancholy prince of Denmark, who spends way too long making up his mind about suicide
or
The smallest of settlements, almost certainly not incorporated except possibly as a joke. Probably just four farm families who decided to build their farmhouses on the adjacent corners of their lots. 100% agricultural.
Village
Larger than a hamlet, and probably (though not necessarily) officially incorporated. Has a few businesses to serve neighboring farmers (at the very least, a post office, a store, an elementary school, and a church), but the dominant industry is still agriculture.
or
A 'burb, development, retirement home, or shopping center that’s trying to sound quaint.
Crossroads
A small settlement at the intersection of two significant through roads, primarily catering to travelers. Has, at the very least, a gas station and a restaurant (probably several), plus possibly a motel or three. Some overlap between this category and villages.
Town:
Larger than a village, and has some major industry besides agriculture, though probably only one employer in that industry. Likely to be the county seat. Has all manner of other businesses, though probably a small selection of each. Probably has a high school/school district. May be further qualified based on the type of industry, such as a college town, mining town, etc.
or
Colloquially, any municipality, regardless of size. One might speak, for instance, of one’s hometown, or going in to town, or the like.
City
Multiple industries, with multiple major employers. Has multiple zip codes/post offices. Has schools at all levels, and its own public school system. Multiple distinct neighborhoods.
Suburb
A municipality economically tied to and contiguous to a larger city (that is, it either borders the larger city directly, or it borders another suburb of the city).
Metropolis
A city with suburbs. Tend to be large, but not necessarily.
Bedroom Community
A suburb which was built deliberately as a suburb. Has no significant industries of its own; most residents work in the metropolis or in one of the other suburbs.
The 'burbs
Bedroom communities composed entirely of planned developments, rather than neighborhoods. Houses all look the same, and are generally under the sway of homeowners’ associations.