Distance measuring is done by ranging. It's a well-established word with millions of hits on Google. Even the well-known radar originally stood for "RAdio Detection And Ranging".
Survey(ing) is a much broader term. It also measures horizontal and vertical angles, elevations, GPS coordinates, etc. Surveying is determined not by the tool, but by the goal — making a space model of something big, but not too big. A house or a land plot are subjects of surveying, but not a continent, which is the subject of another subdiscipline of geodesy, named astronomical geodesy. As for bacterias, they are measured by micrometry, if I remember correctly.
Metrology measures anything for the improvement of the tools and standards for the actual measuring. That includes distances, but also time, angles, temperature, current...
Geometry in the original sense was the same thing as survey today.