What is a street? What is the difference between a street and a road?

A street is a road with houses along it on the two sides or one of the sides. A road is a street that connects two points. For example, Lewisham Road tell us that the road leads us to a community called Lewisham. Lewisham Street tells us that the road belongs to Lewisham. Walworth Road tells us that from Elephant and Castle, the road leads to Walworth. A street and a road cannot be differenciated by size or lenght or how busy the raod is but by principle behind it. At times the two are used intermitently. For example, Jamaica Road in South East London, UK, does not lead us to Jamaica and Market Street leads to the market in Elephant and Castle, London, UK.

A road is a public space where every user has the right to usage, seing, feeling and sensing irrespective of his/her residence, on the other hand a street has right only to the residents of that neighbourhood and this right has to be protected by authorities in the public interest.. No person/group of persons shall be allowed to obstruct this interest to the public.

I like Babar's explanation, and Jose's idea of public space. For us it is a naming tradition, with a street being a bit more of a main feeder into a suburb, or being a main street on a central city grid, and then roads being smaller offshoots of streets (at least in some cases). Added to streets and roads, we have a hierarchy of drives, avenues, crescents, and cul-de-sacs (although that last one doesn't get put into the name usually). I guess it's confused because planners in South Africa derive their references from the US, UK, Netherlands, France, etc, where there are more coherent traditions. Spain, Italy, Brazil seem to have better nomenclatures for boulevards, squares, piazzas etc. There is decent article with some historical references at http://en.wikipedia.org/wiki/Street_or_road_name

A road is a surface used to travel from place A to place B (as quickly and comfortably as possible).
A street is a space along and off which activities are located - and people go to a street to do something (at their own pace).

You travel ON a road, but GO TO a street

To your first question, the Wikipedia defines street as "a paved public thoroughfare in a built environment".
However, I am very fond of the definition given a long time ago by Ildefonso Cerda, a Spanish 19th century civil engineer who was one of the fathers of modern urbanism and planned the extension of Barcelona to what it is today. He said that "the street is both the public thoroughfare and the appendix and complement to each of the houses built aside".
Regarding the second question, i.e. the difference between "street" and "road", I must say English is not my mother tongue, but I gather "road" is closer to the cold definition of a "paved public thoroughfare" than "street" is.
All the best, Jose