Rail was laid in both directions. By 1879, it made it the 22 miles from Chester County to the Catawba River but did not cross it. On the other end, rail was laid from Cheraw to Pageland before the capital was exhausted in that direction. The railroad was operated in these sections and rail was laid across the river and into Lancaster. This created the 29 mile line that would eventually become the L&C.
Meanwhile, efforts were made several times to connect the two lines. The charter of the Chesterfield and Lancaster Railroad Company was approved December 24, 1889 and amended on October 12, 1901. Other efforts were made in the first decade of the 20th century, but track never made it further than Crowbuck. Eventually, the railroad stopped trying to advance and never made it to Lancaster.
Even though it never connected to the Lancaster and Chester as planned, it did operate with some success apparently. Pageland boomed economically in the early 1900s as the Blakeney Hotel was built as well as a railroad depot. The Seaboard Air Line began operating the railroad in 1913 and bought it outright in the 1920s, but by 1941, service ended on the line and the rails were pulled up.
From Cheraw on the SAL, the line went through Excelsior, Thompson, Evans Mill, Rivers, Chesterfield, Caloe, Ruby, Mt. Croghan, Maynards, Guess, Magnums, Pageland and ending in Crowbuck.
According to the Abandoned Rails web site, some small sections of track did survive and can be located with a bit of investigation. Supposedly track does still exist near a mine in Crowbuck, but for the most part, the original Right Of Way is understandably hard to make out some 70 years after the rail was pulled up.
If you go to the Abandoned Rails site listed in the Sources section, there is a map that shows where the ROW went. It seems to be on top of a present day map.
The Chesterfield and Lancaster RR and the Cheraw and Chester RR are totally unrelated lines, built by two different groups, at two different times. The C&C was to connect the two cities [1872] of Chester and Cheraw but stopped at Lancaster. The standard gauge C&L was built in 1907 with intentions of reaching Lancaster, but not to the C&C/later Lancaster & Chester, which was narrow [3'] gauge. The C&L was built by and for Capt. Dolly Page primarily as a lumber outlet to Cheraw.