Keith - yes, now you've got it! These days, smart people are advocating the term **short map** for a map \\(F\\) with
\[ d'(F(x),F(x')) \le d(x,x'). \]
The term ["nonexpansive map"](https://en.wikipedia.org/wiki/Metric_map) is more traditional, but "short map" is descriptive and... short. People often use ["contraction mapping"](https://en.wikipedia.org/wiki/Contraction_mapping) for a map with
\[ d'(F(x),F(x')) \le k d(x,x') \]
for some constant \\(k < 1\\).