Same formula, different substance

Two compounds can share a formula to the last atom and still be different things. Leucine and isoleucine are the standard example: C₆H₁₃NO₂ both, 131.09463 Da both, and no balance or mass spectrometer can tell them apart. What separates them is wiring and geometry.

Constitutional isomers: different wiring

In leucine the side chain branches at its second carbon; in isoleucine it branches at the first. Same atoms, different connections. They are different compounds with different biochemistry, and only the connectivity can tell them apart.

Stereoisomers: different geometry

Fix the connectivity and there is still more than one molecule. Leucine has one stereocentre and therefore two mirror-image forms, L and D. Isoleucine has two stereocentres and four stereoisomers, of which only (2S,3S) is the one found in proteins. A drawing without wedges, or a SMILES without @, describes all of them at once.

One substance, several spellings

Even one specific molecule can be written several ways. The neutral form and the zwitterion are the same substance. Two SMILES strings can encode the same structure in different orders. This is why databases assign a stable identifier (a ChEBI ID, an InChIKey) and compute a canonical form, so that “the same thing” can be checked by a machine rather than by eye.

What a formula is good for

Everything downstream begins with it. The formula gives the exact mass to search for, the number of rings and double bonds, and the elements present. Given a measured mass and enough resolution, a formula can be assigned uniquely. The structure then has to be established by other evidence: spectra, synthesis, or a crystal. Reading a line drawing covers what the drawing itself can and cannot say.