What are robber barrons and captains of industry, referring to the gilded age? What are the positives and negatives of each side?Self Explanatory.
The industrialists of the time period help to reveal much in the way of how individuals view history. I have always felt that the analysis of industrialization reveals much in the fundamental bias of individuals and their perception towards historical dialectics. For example, if individuals felt that industrialists like Morgan, Carnegie, or Rockefeller were "captains of industry," it is likely that they would feel that such figures were critical to the formation of the United States. They would point to how these figures emerged on the scene and carved out a successful niche for themselves, representing the realization of hard work, grit, and determination. Such a view favors a "consensus" view of history where such historical figures represent the very best of American Exceptionalism.
The flip side would be if these individuals could be seen as "robber barons." Instead of being praised, such historical figures have to be scrutinized and analyzed as to how they acquired their wealth. This would reveal that there was a great deal of power consolidation, unfair business practices, and an overall perception where economics trumped all else. Workers' rights, fair compensation, and a sense of empowering the democratic order was overruled in the name of profit generating motives. In the final analysis, this view of history is more of a "conflict" based one where history is an ongoing dialectical process of power consolidation, and more voices, particularly those who are silenced as a result of power, need to be heard. The "Robber Barons" perspective is an example of this, most notably seen in the works of Howard Zinn.
The two terms you give are terms for the same thing, but from different points of view. Both terms refer to people of the Gilded Age who got very rich through business dealings. Those who liked them called them captains of industry, those who didn't called them Robber Barons.
To some extent, both terms are accurate. They did get much of their money through pretty cutthroat practices that did hurt people. On the other hand, the industries they led helped make the US economy grow and helped make the US a more prosperous and powerful country.