The map carries the high points of countries and mountain ranges, and shows more peaks the closer you zoom. The list beside it holds whatever is on screen.
The catalogue holds over a million summits, and drawing them at once would leave a solid smear rather than a map. Zoomed out it therefore carries only the high points of countries and of the largest mountain systems, and adds the high points of smaller ranges as you close in. From zoom level eight it shows everything inside the viewport, tallest first.
For one named range and its boundary, its own page is the better place: it draws the outline of the range together with its sub-ranges. The full hierarchy is in the catalogue of mountain ranges, and peaks by country and continent are in the list of mountains.