While I've not heard of the "C" notation previously, "n" is common notation that indicates the ploidy of a cell. The "n" refers to the number of unique chromosomes within a cell. Eukaryotic cells are generally diploid, or 2n. The multiplying number - "2" in the diploid case - refers to the number of versions of each unique chromosome. For example, humans are diploids (2n). We have 23 unique chromosomes (22 regular chromosomes and 1 sex chromosome), but we have 2 variants of each chromosome to give us a total of 2*23 = 46 chromosomes.
Prior to S phase, diploid cells contain 2n content (maybe "content" refers to "C" notation?) of DNA. During S phase the cell duplicates its DNA content generating 2 sets of 2n chromosomes (2 copies of 46 chromosomes for a total of 92 chromosomes in the human case). You are correct in that it is 2 sets of 2n rather than 4n, since the convention would indicate 4n as a tetraploid (many types of plants are in fact tetraploid, https://en.wikipedia.org/wiki/Polyploid).
At the end of the mitotic cell cycle, cell division functions to separate the 2 sets of 2n chromosomes into two distinct cells, each containing 2n chromosomes. If all 4 chromosomes separated from each other and the cell was able to divide into quarters rather than halves, that would yield 4 1n cells. This latter idea is what occurs in meiosis.