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Fructose is a six-carbon ketose monosaccharide with the same molecular formula as glucose, but different connectivity in the open-chain form. In aqueous chemical solution, fructose occurs mainly in cyclic forms.

Fructose supplies one of the two sugar units in sucrose and is the repeating building block of many fructans. These examples distinguish a free monosaccharide from its residues inside larger carbohydrates.^[ref]

John E. McMurry is the author of an organic chemistry textbook that connects molecular structure with reaction mechanisms. Its treatment of carbohydrates, for example, distinguishes open-chain aldoses and ketoses from the cyclic structures prevalent in solution.

That distinction explains why classifying glucose as an aldose does not imply that most dissolved glucose molecules expose a free aldehyde group.^[ref]

A ketose is a monosaccharide whose open-chain form contains a ketone group. Fructose is a familiar example, with a carbonyl group at carbon 2 in its open-chain structure.

A ketose can form cyclic structures by reaction of its carbonyl group with one of its own hydroxyl groups. The distinction from an aldose concerns carbonyl connectivity, rather than simply the number of carbon atoms.^[ref]

A monosaccharide is a single-unit carbohydrate that cannot be split into smaller sugars by hydrolysis. Ribose, deoxyribose, and glucose are examples. The unit is a whole molecule containing many chemical atoms; a disaccharide instead contains two linked monosaccharide units.^[ref]

Classification combines carbon count with open-chain connectivity. An aldose has an aldehyde group; a ketose has a ketone group. Thus glucose is an aldohexose, while fructose is a six-carbon ketose. These names describe the open-chain reference forms even when cyclic forms predominate in water.^[ref]

Check the distinction by counting the groups in the drawings. Open-chain glucose contains one $\mathrm{CHO}$, four $\mathrm{CHOH}$ and one $\mathrm{C}{\mathrm{H}}_2\mathrm{OH}$ group. Open-chain fructose contains two $\mathrm{C}{\mathrm{H}}_2\mathrm{OH}$, three $\mathrm{CHOH}$ and one $\mathrm{C}=\mathrm{O}$ group. The respective hydrogen totals are $1+4(2)+3=12$ and $2(3)+3(2)=12$; each structure also has six carbon and six oxygen chemical atoms. Their shared molecular formula ${\mathrm{C}}_6{\mathrm{H}}_{12}{\mathrm{O}}_6$ therefore cannot identify the carbonyl group position or the stereochemistry.

The beauty is that a familiar sugar name can embrace an interconverting family of forms. Monosaccharide ring-chain interconversion connects those drawings to mutarotation, a change visible with polarimetry. Spatial arrangement also matters to biology: an enzyme's active site encounters a particular arrangement of hydroxy groups, rather than merely an inventory of chemical atoms. The existing enzyme and chirality articles explain that recognition principle.