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A cholesteric liquid crystal is locally nematic but its nematic director rotates helically, for exampleThe sign of $q_0$ specifies handedness and $p$ is the full-turn pitch. The sketch shows rods rotating through transverse planes. This is helical orientational order, not a smectic density-layer lattice. Although an apolar director repeats physically after a half-turn, the conventional pitch denotes a full $2\pi$ turn. A pitch comparable to visible wavelengths can give selective reflection.

A liquid crystal has some molecular order while retaining liquid-like motion. The distinction between orientational and positional order separates its main phases.

A nematic liquid crystal has long-range orientational order about a nematic director $\mathbf{n}$, with $\mathbf{n}$ and $-\mathbf{n}$ equivalent for apolar molecules, but no periodic density lattice. Its nematic order parameter is $S=⟨(3{\cos }^2\theta -1)/2⟩$, where $\theta$ measures molecular alignment with the director. A cholesteric liquid crystal is a chiral nematic whose director rotates in space, producing a helical pitch while remaining locally nematic.

A smectic phase adds a periodic density modulation in one direction, forming layers with liquid-like motion within each layer. In a smectic A phase, the director is perpendicular to the layers; in a smectic C phase, it is tilted relative to the layer normal. A columnar liquid crystal instead has columns with a two-dimensional positional lattice and comparatively fluid motion along them.

These orders have different experimental signatures. Birefringence under crossed polarizers reveals orientational anisotropy, while X-ray diffraction can detect a smectic layer spacing $d$ through a peak near $q=2\pi /d$. Optical anisotropy alone does not establish a layer lattice.