= Solution
An <absorption line> depends on the population of its lower atomic level, ionization state, transition strength, pressure and broadening, not just elemental abundance. <Boltzmann distribution> changes excitation populations with <temperature>, while the <Saha equation> changes ionization with temperature and electron pressure. Thus similar overall composition can produce very different spectra. Molecules survive preferentially in cool atmospheres.
The <Harvard spectral classification> orders the main stellar classes by decreasing effective temperature: \b[O, B, A, F, G, K, M], from blue to red. Numerical subclasses run approximately from 0, the hotter end of a class, to 9, its cooler end. An A0 star, near $10^4\,\mathrm K$, has very strong <Balmer series> lines; hotter stars ionize much of the hydrogen and cooler stars underpopulate its $n=2$ level. A G2 star, near $5800\,\mathrm K$, has weaker Balmer absorption, many neutral and ionized metal lines, prominent Ca II H and K lines and the CH G band. An M5 star, near $3000\,\mathrm K$, has strong TiO molecular bands, neutral-metal and alkali features, and weak photospheric Balmer absorption.https://voyages.sdss.org/expeditions/expedition-to-the-milky-way/spectral-types/absorption-and-emission-lines/[temperature sequence and characteristic atomic or molecular features]{ref}
For giant and dwarf stars of the same colour, compare gravity-sensitive line widths and ratios. The giant's larger radius gives lower surface gravity and atmospheric pressure, typically narrower pressure-broadened lines; high-pressure dwarf atmospheres have stronger broad alkali wings and different molecular and ionization ratios. These diagnostics assign a <luminosity class>, such as III for a giant and V for a dwarf. A line ratio or calibrated gravity indicator is stronger evidence than colour alone.
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