I've read in Abdi (2003) that
When the independent variables are pairwise orthogonal, the effect of each of them in the regression is assessed by computing the slope of the regression between this independent variable and the dependent variable. In this case, (i.e., orthogonality of the IV’s), the partial regression coefficients are equal to the regression coefficients. In all other cases, the regression coefficient will differ from the partial regression coefficients.
However, the document did not previously explain what the difference between these two types of regression coefficients is.
Abdi, H. (2003). Partial regression coefficients. In Lewis-Beck M., Bryman, A., Futing T. (Eds.) (2003) Encyclopedia of Social Sciences: Research Methods. Thousand Oaks, CA: SAGE Publications.