I recently learned about DAG-Directed Acyclic Graphs while reading econometrics-related papers. So far, I am used to Structural Equation Modeling for Psychology and Education studies, and DAG looks very similar to the path model analysis, like a structural model without a measurement model. When I searched the difference between DAG and SEM or path analysis, some said there is not much difference between them, while others said DAG has advantages over SEM in representing causality in terms of unmeasured confounders rarely considered in SEM, especially for observational data. However, I am still confused about how I can clearly explain the benefit of DAG over SEM to other people who are used to SEM and unaware of DAG. Some strong SEM advocates argue that SEM can do anything DAG can, but I wonder why DAG is becoming more popular in many fields.
This is not a complete answer, but one important difference is that SEM captures the functional relationship between variables, usually as a linear combination with Normally-distributed residuals, while a DAG only specifies whether variables are dependant, rather than independent.
For instance, consider the diagram below.
In SEM, this would imply specific linear relationships, e.g. $z \sim N(b_1 w + b_2 x + b_3 y, \epsilon_z)$. For a DAG, it would only imply that, e.g. $z$ is dependent on $w, x, y$, without going into additional detail.