On the one hand, you have the economic history approach, which is to label this period as industrialization. Under this framework, technological growth and factor endowments (such as the relative unavailability of land coupled with a surplus of laborers) are the primary variables of interest. For example, Alex Field asks a very simple question: "why did the North begin to industrialize at all?" in "Sectoral Shift in Antebellum Massachusetts: A Reconsideration" (Explorations in Economic History Vol. 15, 1978, pp. 146-71) Field explains industrialization as primarily the result of: 1. technology and available capital (technology initially imported from England, financed by wealthy northeast merchants); and 2. labor surplus (he explains that while agriculture was a more fruitful pursuit outside of the rocky soil of New England, labor mobility in this period suffered important barriers which kept the poor country bumpkins stuck in their villages).
On the other hand, the social history approach uses terms like proletarianization and "industrial order" to describe the exact same period and, at times, the exact same events! First, proletarianization is a concept borrowed from influences on social theory by Marxist thought. Proletarianization describes the processes by which individuals become part of the capitalist social system. In the orthodox approach, for example, proletarianization is a consequence of the increased mechanization of production. This forces workers out of their homes and farms, and "middle class" masters, apprentices, and journeymen out of their shops, into centralized facilities of production (factories). More recent approaches have modified this framework to take into account the variations on this idea, but maintaining the central point that this is a coercive process of integration into a new system -- for example, the fact that workers, while still proletarians, largely did not come from a shrinking middle class. Rather, they were either women and children coming from a household which was still significantly influenced by traditional norms and institutions, or immigrants escaping religious persecution or other types of political or economic oppression in their home countries.
The divide is very significant for understanding the rise of capitalism. It needs to be bridged.
How can we get each side to talk about industrialization or proletarianization using the same terms? The lazy answer would be, "integrate the higher-quality aspects of both!" -- something like a quantitative study of social relations or social transformation, synthesizing the great strides made by the economic historians in establishing the data sets with the more holistic and contextual approach of the social historians.
I, however, have a different proposal. The gap is driven by economists and social historians too focused on the standard models of their respective disciplines. If you read my above clarifications carefully, you'll note that both sides are essentially discussing the history of the early nineteenth century U.S. in terms of slight "variations on a theme".
We need a new melody. While the rhetoric of the rising capitalist class was centered on economic variables like capital accumulation and productivity, laborers sung to a different tune based on control over the pace of work and the rules under which new markets would be governed. In the meantime, the state thundered a baseline centered on a large amount of bureaucratic control influenced by, but also tempering, both traditional aristocratic models of governance (residue from the colonial period) and new liberal models of state intervention appropriate for a republican democracy.
This is not a chaotic model. Each institution has specific goals, and the relevant conflicts and complementarities between them may be sorted out, with reference to the data. The point is then to tell a story which incorporates these goals with the primary evidence in question. The result is an explanation of change which eschews particular definitional requirements in favor of a general model of change.
While I'd like to think something like this -- essentially, the ideas on which my dissertation are based -- will catch on, I'm not holding my breath. For now, I will continue to use either "industrialization" or "proletarianization", depending on the specific questions I am asking and the the specific audience I am targeting. But when it comes to debate, I will open up the field to consider the musical score as a whole. Only then can I work through the language to establish a more appropriate understanding of this period.