three sigma vs six sigma

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I wonder about the meaning of the term six sigma. It describes a process/production with (mostly) zero defects. You can see here:

source: https://www.dummies.com/article/business-careers-money/business/operations/how-six-sigma-can-benefit-your-operations-management-162941

but what I wonder is that, for me, the opposite should be the case: The more sigmas (standard devations), the broader the distribution should become resp. the broader the single “data points” are.

source: https://www.intechopen.com/chapters/17405

So my question is: How/why is six sigma better than e.g. three sigma?

Is it due to the amount of sigmas to reach the LSL/USL?
In case of ~3 three sigmas it looks like one needs, well, three sigmas to reach the specification boundary and for six sigmas it might be six.