From the mathematical perspective, (a) d indicates differential as in differential calculus. For example, y = f(t). Then, dy/dt is differential of y with respect to t. (b) The greek letter delta,  δ is not used much in maths (c) However, we have partial differential concept in maths which uses the symbol dow ∂. If y(f) = f(x,y,z,), then we use partial differential like ∂f/ ∂x etc.

From the physics perspective, (a) d indicates differential as in differential calculus as in maths. For example, displacement y = f(t) dy/dt = velocity and d²y/dt² is acceleration is a common concept known to all of us (b) The greek letter delta,  δ is used in physics to indicate very small change. For example, many times in optics, to indicate angle changes, we use this symbol. Basically, delta in physics indicates very small change. Very rarely, as a misnomer, it is used interchangeably with d as δx representing dx. (c) The symbol dow ∂ is not much used in physics.