In the news

I'm confused, because I see the two circles as being arbitrary shapes used to represent percentages, which should be directly relative to the size of the hypothetical 100%

So say this 100x100mm circle represents 100% of the welfare budget:

This circle is 41x41mm: so is 41% of the size of the entire welfare budget, and the percentage that people perceive goes to unemployment benefits:

And this is 3x3mm: 3% the size of the 100% welfare budget, which is the actual amount spent on unemployment benefits

I agree with skydancer that two pie charts have been much more effective. Or even a bar chart.

You are mixing up your dimensions, the most important thing is the area of these circles, not the diameter (which is also not described as A x B : that is for squares or rectangles). If you double the diameter of a circle you more than double it's area.