First of all, you can use path analysis to examine models that are more complex (and realistic) than multiple regression. However, it can compare different models to determine which one best fits the data. Path analysis can disprove a model that postulates causal relations among variables, but it cannot prove the correlation.
Path analysis is part of structural equation analysis to propose to evaluate explanatory theoretical models in a global way unlike regression analysis which does not allow you to generate causal or global hypotheses.
the path analysis can be understood as a form of multiple regression analysis. In order to be able to make reliable statements regarding complex relationships, the hypothesis system, which has already been logically justified, should be subjected to a path analysis. This makes the relationships clearer. For this purpose structural equations are to be created from which linear systems of equations are developed. These serve to determine the path coefficients and to estimate disturbance variables. As far as the calculation is concerned, structural equations are to be set up only for the variables, to which several arrows point. In the path analysis the correlations are decomposed into their direct and indirect causal effects as well as their non-causal effects. The causal effects result directly from the path coefficients. Furthermore, the direct causal effect on the direct path results. The indirect effect from a detour from the product of the path coefficients. If the direct and indirect effects are added, the total causal effect follows. The non-causal effect is obtained by subtracting the total causal effect from the correlation between the dependent and independent variables.
I would say that a path analysis is a way of setting out regression coefficients in a set of related models. Generally this is done with the aim of modeling causal patterns in the data - though that's controversial. In a classical path analysis the path coefficients are obtained from a series of multiple regression models.
In a SEM path model the model can include latent variables. These models can't be implemented as a series of multiple regression models - but the use of latent variables adds flexibility and complexity to the model.
Applied Regression Analysis: A Second Course in Business and Economic Statistics (with CD-ROM and InfoTrac) (Duxbury Applied Series) [Hardcover] [2004] 4th Ed. Terry E. Dielman by aa | Jan 1, 1994.
Multiple Regression and Beyond by Timothy Z. Keith | Jan 27, 2019
Standard regression analysis (SRA) can be used to estimate models including just one dependent (Y) variable whereas path analysis (PA) can facilitate more than one dependent variable (Y1, Y2,...,Yq). This difference makes PA a simultaneous multivariate modelling technique. When PA includes factors/unobserved variables, it becomes a structural equation modelling (SEM) technique.
"Path analysis is an extension of multiple regression. It goes beyond regression in that it allows for the analysis of more complicated models.
Path analysis can be used to analyze models that are more complex (and realistic) than multiple regression. It can compare different models to determine which one best fits the data. It can disprove a model that postulates causal relations among variables, but it cannot prove causality".
For more details, read
Article Finding Our Way: An Introduction to Path Analysis
Yes, after multiple experiments, I have found that the estimated coefficients remain to be same across linear regression and path analysis model.
One advantage that could be noted is excluding link between specific categories (independent variable) to the dependent variable (continuous or categorical). This helps in reducing degrees of freedom and improving model estimates. However, given that this family of model will fall under gsem, there is no way to assess goodness of fit of the model.
I would be happy to hear about more details regarding the model development using path analysis and assessing goodness of fit for gsem. Any contested views are also welcomed.