As shown in the title. What is the difference between Road, Avenue, and Street?
"A road is a thoroughfare, route, or way on land between two places, which has been paved or otherwise improved to allow travel by some conveyance, including a horse, cart, or motor vehicle."
"A street is a paved public thoroughfare in a built environment. It is a public parcel of land adjoining buildings in an urban context, on which people may freely assemble, interact, and move about."
"In landscaping, an avenue or allée is traditionally a straight route with a line of trees or large shrubs running along each side, which is used, as its French source venir ("to come") indicates, to emphasize the "coming to," or arrival at a landscape or architectural feature. In most cases, the trees planted in an avenue will be all of the same species or cultivar, so as to give uniform appearance along the full length of the avenue."
These descriptions came from https://en.wikipedia.org by searching for "road", "street", and "avenue" - I would have posted direct links to each of these, but need more rep in order to post more than 2 links in an answer. I just found this site today.
So from these descriptions - a road is an improved path between two points whether in areas outside settlements, in the suburbs, or in urban areas, while a street is a paved public path within a built up area, and an avenue is a road or street with trees planted along both sides, generally of the same species for uniformity.
Where I live (Tulsa, OK, American Midlands) there isn't a difference. They are used interchangeably.
In addition to the other good answers here I would add that in some cities these terms are used in a standard manner to indicate direction. In Seattle, where I live, every "Avenue" runs north-south and every "Street" runs east-west. However, that's just Seattle. There are cities where this rules is reversed, and also where there is no standard rule for associating a name with a direction.
In the UK, a road is a general, unspecific term. A street implies an urban (in a town) road. An avenue technically means that it has rows of trees on both sides, but is also used to imply that it's rural - for example the cliche "[Acacia Avenue]"1
Road is the only one of these words in common use outside a town. Within a town or city, use varies by location and tends to have many exceptions, some of which have to do with changing character of surrounding neighborhoods.
Washington, DC, for example, uses (in the main) numbered streets running north-south, and lettered streets east-west. After exhausting the alphabet, the lettered streets continue with two-syllable names in alphabetical order [Adams Street, Bryant, etc.], then three-syllable [Albemarle Street, Brandywine], and finally trees. The original plan was for diagonal avenues named after the states, and most of these are broad, important thoroughfares, such as Pennsylvania Avenue, where the White House is. There are, however, exceptions: Idaho Avenue is a narrow, local residential street. There are also a handful of roads, that do not conform to the grid plan, and which are relics of paths from before that part of the city was urbanized, or which connected Civil War fortifications. Some of these are heavily trafficked and some not.
In contrast, in Berkeley, California, there are parallel small residential streets named Magnolia Street and Pine Avenue, and the choice seems to have been made totally arbitrarily.