There were perhaps more similarities than differences between the two; and the American Industrial Revolution was in many respects an accidental child of the British revolution.
One important difference is that the first major industry in the United States was transportation. The advent of major railroads and steam boats together with the large-scale production of canals in the Northeast shifted the industrial and commercial center of the nation from New Orleans to major ports in the Northeast, such as New York, Boston and Philadelphia. Industrialization created something of a nationwide market, as goods could be transported easily from one end of the nation to the other. The factory system came to America much later with the development of the Lowell System, where all production was done under one roof. This would not have happened had not a British citizen, Samuel Slater, disguised himself to travel to America with the plans for a fully operational textile mill memorized. Upon arrival, he built the first successful textile mill in the Americas in Pawtucket, Rhode Island.
In Britain, Industrialization was born with large scale textile production rather than means of transportation, including the invention of the water frame, flying shuttle, and spinning mule. Ironically, British textile mills were heavily dependent on American cotton for raw materials. Still, Britain closely guarded its textile industry, so much so that it was a crime punishable by death to export parts or plans for textile operations. This made Slater's actions all the more daring, and ultimately damaging to British manufacturing.
In both nations, the invention of the steam engine proved essential to industrialization.