Like galaxyrocker's answer:
Cosán: Any kind of path
Bealach: Can be clearer than a Cosán, and wider.
Bóthar: A rural road, wider again than a Bealach.
Sráid: A road/pathway in a town.
A forest pathway would qualify as a Cosán. A cleared pathway, distinct as a path, is a Bealach. Bóthar is essentially at the level that cars can freely pass in both directions.
Even in English in Ireland a "street" is a purely urban/town thing. I would never call a country road a "street". Perhaps this is different in other English dialects.
Usage varies in the States, perhaps because individual designators such as “road”, “street”, “avenue”, “drive”, “way”, etc. are chosen purely for aesthetic reasons. “Road” can be used here as something that connects two distant places, no matter the width or material of its surface, while “street” wouldn’t; for example, the Crosby/Hope Road to … films would not have been named Street to … . “Railroad” is used much more often than “railway” here.
I think street, avenue, and boulevard are fairly consistently urban, or at least suburban, here in the States. A road can be anything. Threw me for a loop when I first learned about the Roman roads in Britain, like Watling Street and Dere Street, which were long distance paths between cities. Guess they'd be bóithre or at least bealaí.
Outside the US, the pavement is a synonym for what you call the sidewalk - indeed, in parts of the US, pavement is a synonym for sidewalk ("to pound the pavement" implies walking the streets, not driving a vehicle). Footpaths/sidewalks in towns and cities were "paved" long before roadways were.