Actually, although historically classified as an interurban, the South Shore Line really is different from the typical interurban lines. Differences which contributed to the South Shore Line being the sole survivor. The South Shore Line has always had the look of a commuter rail line, using electric MU cars with pantographs. A typical commuter line was originally steam powered, later electrified by the steam railroad. But the South Shore Line was originally constructed as an electric railroad.
Although the South Shore Line entered Chicago over the Illinois Central Railroad, a steam railroad which had electrified its commuter line. The South Shore trains blended in well with the Illinois Central's electric MU trains.
Typically, a railroad could be classified as an interurban if it was originally constructed as an electric railroad, if it handled primarily passengers with little freight traffic, and if it handled little interchange and little interstate traffic. Interurbans could thus generally be exempt from federal regulation by the Interstate Commerce Commission. The South Shore Line managed to remain classified as an interurban, despite heavier than normal freight (which contributed to its longevity).
But a typical interurban used passenger cars which more closely resembled streetcars. Typically, interurban lines were basically extensions of streetcar lines into the country, and on to neighboring cities. In many cases, the interurban and the local streetcar companies were the same.
The typical interurban line would have a single car for each train, typically operating every one or two hours. Because of the low volume handled by an interurban line, a line would need to be constructed economically, usually running alongside roads in the country and including sharp curves, steep inclines at grade separations, and street running in cities. But fortunately, interurban cars could accelerate and decelerate more rapidly than a steam train, so this was less of a problem. Such economical construction, including street running, is perhaps the most significant interurban characteristic of the South Shore Line.
But the South Shore Line was generally constructed somewhat better than the typical interurban lines, including private right of way in the country. Also operating in the South Shore Line territory were a couple of more typical local interurban railways, Gary Railways and the Northern Indiana Railway. Those companies also provided local streetcar service in the cities served, and abandoned their interurban lines in the 1930's, as typical for lines of that nature. The South Shore Line was better suited for high speed trains with multiple cars, and operated directly into downtown Chicago, also contributing to its longevity. Similarly, the North Shore Line and the Chicago Aurora & Elgin were able to last longer than typical interurbans, by providing high speed service directly into downtown Chicago. Although those lines used somewhat more typical interurban cars, though with most trains using more than one car.
So in trying to understand the electric interurban railways of the past, one must remember that certain interurban lines were the most successful and longest lasting, because they were not like the typical interurbans.