This statement is accurate, but only to a degree. The New Deal was similar in some ways to the Progressive agenda, but in other ways it went well beyond that agenda.
The New Deal and the Progressive agenda were similar in that they both tried to protect workers from the ways in which employers could abuse them. The Progressive movement pushed for things like minimum wages and worker safety laws. The New Deal wanted to make it easier for unions to organize and to work effectively for workers’ rights.
However, the New Deal went beyond this. The New Deal was much more interested in using government to positively impact the economy as a whole. The Progressives did not aspire to this. The Progressives did not contemplate using governmental power to try to determine how much farmers could produce. It did not contemplate having the government subsidize various industries. In these ways, the New Deal was much more ambitious in terms of the economy than the Progressive movement ever was.