Order topology is the same as the metric topology on $\mathbf{R}$?

The wikipedia article for the real line says that the order topology and the metric topology of the reals are the same.

What is the explanation that these two topologies are in fact identical?

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They both have the same basis: the family of all open intervals $(a,b)$, where $a$ and $b$ are real numbers with $a < b$.