reading about the Wild West and concluding that the American Revolution happened in the 1870s or so. After all there are all of these references to America about then. What you're missing is that a revolution marks a boundary. America was around in the 1870s but the boundary of its existence was a century earlier. (It is traditional to say that America began with the signing of the Declaration of Independence in July 4, 1776. That's wrong, but let's not get sidetracked.)
The same applies here. Yes, lots of industrial stuff happened at the same time as the Titanic. That is because the Titanic happened during the Industrial Age. But we're still in the Industrial Age. (ie the era where our economy centers around industry and manufacturing.) The Industrial Revolution happened at the boundary of that Age. Of course that transition happened in different places at different times. But it is traditionally held to have happened in England around 1760-1830, and elsewhere in Europe and America 30-100 years later. (It is still happening in some parts of the world.)
So you're off by about a century, give or take some decades.
Cheers,
Ben