Chromosomal structures in S phase and Prophase
A comment by user AlwaysConfused has answered one part of the question, but I think that the OP's confusion is related to a point of language or teaching. The number of chromosomes doubles during S phase (C number), but the ploidy of the cell does not change (N number). That's what your textbook is trying to tell you, it's just stating it fairly confusingly.

When we say that there are the same number of chromosomes before and after S phase, that's just a lie that we tell ourselves to keep from getting confused. We have invented the C vs. N terminology that AlwaysConfused mentions to try to handle this: we say that the 2N of a diploid cell remains constant across the cell cycle, while the C number alternates between 2C (before S phase) and 4C (after S phase).

For you, this confusion seems to be worse because how we represent chromosomes is not what chromosomes actually look like, and this has gotten mixed up with the definitions of chromosomes.

When we draw pictures of chromosomes we draw them neatly like they are in mitosis, but that is not at all what they look like in interphase. They are still chromosomes during that time, they just aren't pretty and neat ("condensed").

To sum it up more, here is a diagram of chromosomes in interphase (most of the time) vs. during mitosis: 

It is only during a very specific part of the cell cycle (mitosis) that the chromosomes are packaged up ("condensed") in such a way that we can readily see them as discrete entities. The rest of the time they're all glommed together and are organized instead according to transcriptional activity etc. rather than according to which molecule they're part of. Remember: chromosomes are very big molecules and if they are "loose" they have a total length that is many orders of magnitude larger than the diameter of the nucleus; so the nucleus is like a big bowl of noodles in interphase.

In S phase it will just be a bowl with twice as many noodles in it as before, because there are twice as many DNA molecules ("chromosomes"; "chromatid" is a term that only applies to the condensed form in mitosis).