In Europe, trains are ubiquitous. It is possible to travel between virtually any cities by rail. Furthermore, railroads are used to transport cargo extensively. The United States has almost no national railroad infrastructure for long-distance passenger travel, and relies extensively on road trucks to transport cargo. What is the reason behind this discrepancy? I would assume that massive railroad infrastructure networks are much more efficient and convenient once developed.
I worked for one of the large Class One Railways in the US: BNSF, although it is part of Berkshire Hathaway. I have also read up on the history of railroads in the US. I might be able to clear up some misconceptions you seem to have.
As a disclaimer some statistics/figures may infringe on the "20 year" rule. The track may have been put in more than 20 years ago but still exists today and thus impacts statistics from today.
The US transports ~40 percent (by weight) or ~20 percent (by value) of cargo by rail (we tend to transport heavy stuff by rail). Europe is only at ~8 percent (by weight). I couldn't find a source for the "by value" percentage in Europe. I also assumed that by "Europe" we can just consider the EU. Ultimately, US freight rail seems to be well developed. This is partially because of the deregulatory Staggers Rail Act that was passed in 1980. This act allowed US railroads to charge market prices and to have much more freedom in determining the rout that the cargo took. European railways are primarily publicly owned and have some operational differences that increase costs, namly separating the commercial part and the construction and maintenance part.
Europe does transport many more people, both as a percentage and in raw numbers, much faster than the US passenger rail system. Both the US and european passenger systems are publicly owned. In the US passenger rail and commercial rail was privately owned until the 1971 when the Rail Passenger Service Act was passed. This Act allowed for public funds to be used to help the struggling US passenger lines. The reason the passenger lines were in trouble was that the US highway system contributed to a decline in ridership.
One point that gets brought up is that Europe has much more high speed rail than the US. The US does have some high speed rail, the Acela Express, built in the 1990s but the European high speed rail is much more extensive and faster as the US line is also used by slower passenger transport. Freight rail can't use high speed rail lines. The freight cars are much heavier and the maintenance issues would result in the "high speed" cars traveling much closer to normal speed.
In conclusion: the US is quite good at moving heavy cargo by rail and does this a lot. The US has not invested in passenger rail as much as Europe for a variety of reasons. I hope this gives you insight into rail infrastructure in the US and Europe.
Sources:
The Great Railroad Revolution, by Christian Wolmar
https://www.bts.gov/newsroom/2017-north-american-freight-numbers
https://www.gpo.gov/fdsys/pkg/STATUTE-84/pdf/STATUTE-84-Pg1327.pdf
The united states is huge and less densely settled; running rail roads is expensive and requires going a lot farther to connect areas. Also, the expense of acquiring private land to build railroads through eminent domain is exorbitant due to the extraordinary cost and delay of litigation. Further, there was a much bigger push for roads and private transportation than mass transit. Because Blacks could not vote in the south, money was devoted to projects that benefited white suburbanites-IE highways and roads-over things like subways and rail transit.
Where jurisdictions try to invest today it's now too expensive. For example, Atlanta, where I live now, is trying to expand its transit system. In the prior 40 years, whites blocked investment in a public transit system that overwhelming would benefit blacks in Atlanta. Voters-IE whites-ensured money was spent on highways and bridges in rural Georgia not the big city. Now that it's a crisis in Atlanta and the state is ready to invest in Atlanta public transportation (for the first time ever), the cost per mile of track is astronomical. It's much cheaper to add buses.
You see the same patterns in big cities all over the south where whites blocked infrastructure programs in major, majority black, cities.