scaleRank in all Natural Earth themes indicates at what scale (zoom) the feature should appear on the map.
See: http://kelsocartography.com/blog/?p=2407
With the caveat that NE has a scaleRank that equates to 1:50,000,000 that puts the sequence 1 out of order mid way thru.
For most features, the zoom their geometry should be drawn on the map, and the zoom which they should be labeled (or fully labeled versus abbreviated labeled) is the same. For the situations where this is not true, labelRank comes into play. This is more helpful for countries than populated places. If scaleRank is not fully getting you there, pursue labelRank.
Both these attributes are based on relative importance of cities based on a variety of factors. Not purely what type of administrative capital or raw incorporated population. For instance, Washington DC is less than 1 million people, but is the central city for a metro area of over 4 million and is an important world city.
You likely see the labelRank here as an intermediate step I’ve been making to refine the scaleRank values further.
More on attributes: https://www.naturalearthdata.com/forums/topic.php?id=40
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