$\begingroup$I've been looking for a definition of this term in everyday words but I can't come across one, the use of the word is in the context of Isometrics.
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$\begingroup$If $d_X$ is a metric on a space $X$, and $d_Y$ is a metric on a space $Y$, a function $f:X\to Y$ is said to be distance-preserving if $d_Y\big(f(x),f(y)\big)=d_X(x,y)$ for all $x,y\in X$: the distance between $f(x)$ and $f(y)$ in $Y$ is always the same as the distance between $x$ and $y$ in $X$.
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