I'm new. Just reading the useful answer to a question about shared centimorgans of first cousins with different paternal grandmothers. I share 238 cM with a second cousin. We can be pretty sure that we share the same great grandmother, but it's possible that she had children by different fathers. With this amount of shared DNA, is it possible that our great grandfathers could have been different? ie could we be half-second cousins or is it more likely that we share the same g grandfather? I share 270 cM with another second cousin (on a different side of the family) where the identity of our g grandfather is not in doubt.
213 cM is the expected value for a full 2nd cousin while 106 cM is the expected value for half 2nd cousin. So sharing 238 cM is entirely consistent with being full cousins.
The Shared cM Project https://thegeneticgenealogist.com/wp-content/uploads/2017/08/Shared_cM_Project_2017.pdf provides a good statistics for the amount of DNA is shared using reported known relationships. What I find more useful from this chart is that it also includes the range of reported shared DNA (excluding outliers)