What type of third party are the populist party and the greenback party considered to be?

Both the Greenback and Populist parties are Economic Protest parties. The Greenback party (1874-1889) was anti-monopoly, former agrarian party that attempted a farmer-labor coalition and the Populist Party (1887-1908) which was hostile toward the elite, banks, railroads and promoted a radical agrarian ideology.

They were considered left wing protest groups. They did not like the way the other two parties were going so they started up their own. They are considered to be those that broke away from the two major political parties.