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The question arose in the comments here.

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Linguistic distance is not a really well-defined term. When you consider a tree model of language evolution (this assumption is contested, e.g., by wave models of mutual influence) you can define linguistic distance as the time since the split from the last common predecessor. You can imagine different methods to measure or aestimate this time.

Lexical distance is one of these methods. It assumes a more or less constant replacement rate for core lexical items over all languages (Again, a contestable hypothesis).

An alternative method to Lexical distance measures the amount of sound changes in cognate words (see my answer here).

A problem with a tree model based linguistic distance is that it cannot measure linguistic convergence (e.g., the formation of a Sprachbund).

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Lexical distance (based on methods as Levenshtein distance) serves to determine the linguistic distance. It is the first step to elaborate a classification of linguistic varieties (they can be displayed as tree). So lexical distance is tied to linguistic distance. Without that we can use other linguistic facts (phonemes, syntactic order, ...) in order to elaborate other kinds of distance (for example phonemic distance, based on their distinctive features). But the morpheme is the linguistic fact the most used, that is why lexical distance is often associated with linguistic distance. Now, the discipline that studies the linguistic distance is called dialectometry.

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