Similarities and analogies between the $E, P$ and $D$ fields with the $B, M$ and $H$ fields and their limitations

In the course of my learning electromagnetism, I’ve noticed there are a striking amount of symmetries in electrostatics and magnetostatics, almost down to replacing divergence operators with curl operators. For instance,

$$vec P = epsilon vec E$$
$$vec H = mu vec B$$

For linear media, and

$$vec D = epsilon_0 vec E + vec P$$
$$vec B = mu_0 (vec H + vec M)$$

And where $vec H$ is defined, at least in Griffiths, in a completely analogous way to electric displacement, save for the typical curl operator that is usual for magnetostatics and a current density instead of charge density.

I am tempted to say that the effects of polarization and magnetization are totally analogous, that “$vec H$ is basically the magnetostatic equivalent of $vec D$” since I have far more trouble visualizing magnetization than I do polarization so if I can get away with thinking this way it’d make my learning easier I think. Do I have it wrong? Am I justified in thinking things in terms of analogizing from polarization? Am I oversimplifying things massively? Be as pedantic as you’d like.