In physics, all formulas are equations, but not all equations are
formulas. (Oddly, let's include among "equations" some inequalities!
E.g., the uncertainty principle.)
In physics, an equation becomes a formula when the equation has
general validity. I.e., when it applies to a large class of
situations. Some laws and principles are expressed as formulas.
But now what the heck distinguishes a law from a principle? Is a
principle a particularly comprehensive law?