DNA is a long fiber construct that looks like a strand of hair, and a chromosome is a product of DNA.
''So, what do you understand by DNA anyway? DNA can be described as a long fiber that resembles a hair under a powerful microscope. The only difference is that they are much thinner and longer. The whole structure is made of two strands that are intertwined together. When cells get ready to divide, proteins attach themselves to the DNA and leads to the creation of a chromosome.
A chromosome is simply the product of the DNA and the proteins that are attached to it. There are 23 pairs of the chromosomes in every human being. One set is inherited from the father, and one set is inherited from the mother. A DNA is a sort of a bio molecule. The entire DNA in cells can be found in individual pieces that are called chromosomes.
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Hope i helped :)
Source: http://www.differencebetween.net/science/health/difference-between-dna-and-chromosome/