TLDR: White circles are CO2e emissions per 10m people. Black dashed rings and colorful dashed rings show the "fair share" emissions for a single country.

Yeah... in hindsight, the distinction between the white / black circles isn't strong enough.. and there's too much distinction between the black rings and the colorful rings, which are conceptually equivalent.

If you look close, you can see that the black rings are actually dashed rings. They show "fair share" for lesser emitters, so they're the equivalent to the larger colorful, dashed rings for the top 10 emitters. So to show fair share, there are 10 colorful-dashed rings for the top 10 countries and ~220 black-dashed rings for the other ~220 countries.

On the other hand, the white-circle puffs represent actual emissions. Each white-circle puffs show 29 years of emissions, per 10m people from a particular country. This is like cumulative per-capita emissions (so white-circles for a given country are all the same size). Each country has one white circle for every 10 million people (or one proportionately smaller circle for countries with <10m people). So there are ~650 total white-circle puffs for the average ~6.5B world population. The smokey background for the puffs are mainly for mood/tone and differentiating the top 10, but they're also meant to connect the puffs since packed circles leave some gaps.

The idea with the white-circle puffs was that, if we arrange the puffs in a loose hexgrid, the area for all puffs would sum to roughly the area of total emissions for that country, in a way that's comparable to the fair-share rings... and the area of all 650 puffs (including lesser emitters) should sum to the area for total global emissions.

So, for example, the average population for Canada over the period was like ~30 million people, so Canada has 3 white-circle puffs. Canada emitted 4x its "fair share" of CO2e, so you can see that each white-circle puff is quite big, and the total area of their 3 puffs is ~4x the area of their dashed-fair-share ring.