In some ways, the New Deal and the Progressive Era were similar. The Progressive Era saw the beginning of government involvement in the economy and the New Deal took that to new heights. The New Deal really cemented the idea (which had started in the Progressive Era) that the government was responsible for making the economy run well and fairly.
However, the New Deal was (when compared to the Progressive Era) much more about economic stability and much less about economic justice. The most important changes in the Progressive Era involved things, like trustbusting, that were meant to reduce the power of big businesses and to prevent them from abusing the people.
The New Deal was not like that. The New Deal did not try to punish businesses or to stop them from hurting people. Instead, the New Deal was meant to create economic stability. The New Deal featured projects like the TVA which were meant to promote growth and stability. It featured new programs like Social Security and the FDIC which were also meant to protect people against economic pain, but not really meant to protect them from the actions of big business.
All in all, then, the Progressive Era was more about reining in businesses and preventing them from abusing people whereas the New Deal was more about helping to keep the economy stable, which would help both individuals and businesses.
The New Deal differed from the Progressive era because the New Deal involved a much greater investment of the federal government in providing direct help to people and involved the development of a more intricate government bureaucracy. During the Progressive era, the government passed legislation, such as the Pure Food and Drug Act under Teddy Roosevelt, which protected consumers from quack medicines and tainted food, or the Clayton Anti-trust Act under Wilson, which added teeth to existing anti-trust legislation. However, under the Progressives, the government was not involved in creating jobs or giving direct handouts to people on relief.
During the Great Depression, however, the federal government provided employment directly to people through agencies such as the Civilian Conservation Corps and the Public Works Administration. The government also provided relief money to people through agencies such as the Federal Emergency Relief Administration.
The goals of the New Deal were relief (meaning helping people in need), recovery (getting the economy moving again), and reform (changing the government's management of the economy through acts such as the 1933 Banking Act that established the Federal Deposit Insurance Corporation or FDIC). However, the Progressive era legislation mainly focused on reform, not on relief or recovery. The government was more directly involved in the lives of Americans during the New Deal than during the Progressive era, and during the New Deal, the role and size of the federal government grew.