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Local thermodynamic equilibrium (LTE) is a condition, e.g., of a gas, such that the variation in temperature is small enough that "constant temperature" is a useful approximation, i.e., it can be usefully treated as if in thermodynamic equilibrium (TE). If processes under study directly affect matter only within sufficiently short distances, then such an assumption of constant temperature can be a useful approximation. The term is also used for the model that assumes the condition.
The term NLTE (for not or non-LTE or non local thermodynamic equilibrium) is used for an amended LTE-like model that accommodates a common discrepancy from true LTE, specifically, excess electromagnetic radiation invading the locality. Like LTE, it is an approximation used to make stellar models (and other models) tractable. The terms kinetic equilibrium and statistical equilibrium are sometimes used as an alternative to "NLTE" since someone could mistakenly take the term NLTE to mean "global thermodynamic equilibrium" or to mean any other condition that doesn't comply to LTE.