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Stereochemistry studies the spatial arrangement of chemical atoms in molecules. A Fischer projection records this information at successive stereocenters, whereas a molecular formula only counts chemical atoms. See McMurry: representing carbohydrate stereochemistry.

A chemical substance with the same molecular formula as another but a different connectivity of chemical atoms.

In chemical usage, sugars commonly means small carbohydrates, including single-unit monosaccharides and two-unit disaccharides. Glucose, ribose, and deoxyribose are monosaccharides. Cellulose is instead a polysaccharide assembled from many glucose units. The distinction counts chemically linked units; it does not classify every carbohydrate by sweetness or biological role. See Clark, Douglas and Choi, Biology 2e, 3.2: carbohydrates.

A useful first description of a monosaccharide asks how many carbon chemical atoms it contains and what its open-chain structure is. Ribose is an aldopentose, a five-carbon aldehyde sugar; glucose is an aldohexose, with six carbon chemical atoms. A Fischer projection then records the stereochemistry, information missing from the molecular formula. See McMurry, Organic Chemistry, 25.1: carbohydrate classification.

Urea is the chemical compound with molecular formula ${\mathrm{CH}}_4{\mathrm{N}}_2\mathrm{O}$ and structure $({\mathrm{NH}}_2{)}_2\mathrm{CO}$. See the NIST Chemistry WebBook, urea: formula and structure. Concentrated urea is used to promote protein denaturation in the ribonuclease A refolding experiment.