Correlation is a form of regression. Both are appropriate for estimating the degree of relationship between two continuous variables. The only difference is that a full model regression will allow one to enter more than one 'control' variable.
As Rhiannon says, there isn't really any fundamental difference - though it is true that regression equations can have multiple predictors, while correlation is more limited (partial correlations, though, approximate what is achieved by multiple regression).
I think the answer to your question boils down to the functions for which the two techniques were developed. Correlation is intended to estimate the relationship between two variables at a point in time. Regression is intended to estimate how well one variable predicts another. Siblings, of course, are of the same generation, so correlation makes sense. While parents precede children, so regression (prediction) makes sense.
If you are trying to compare results across the two types of analysis, remember that the beta weight in a regression equation is the same as a correlation coefficient.