chromatin
Think of the genome as several meters of fine thread that must fit inside a cell nucleus only a few thousandths of a millimeter across. Chromatin is the solution: the DNA woven together with packaging proteins into a flexible, spool-and-string material that can be coiled tightly when storage matters and loosened when the cell needs to read its genes.
Chromatin is built from DNA wound around clusters of histone proteins, forming repeating beads called nucleosomes, which then fold into thicker fibers. Biologists often distinguish two states: euchromatin, which is loosely packed and generally accessible for gene activity, and heterochromatin, which is densely compacted and mostly silent. The same stretch of DNA can shift between these states, and that switching is a major way cells control which genes are turned on.
Chromatin and chromosome describe the same underlying material at different moments. During most of a cell's life the genome exists as diffuse chromatin spread through the nucleus; only when the cell divides does the chromatin condense into the discrete, visible chromosomes. Chemical tags added to the histones and to the DNA itself can alter how tightly chromatin packs, a layer of regulation studied under the heading of epigenetics.
Euchromatin (open, active) and heterochromatin (compact, mostly silent) are not permanent labels; a region can be remodeled from one to the other as the cell's needs change.