So, I understand the total derivative is used when you cannot hold a variable constant, for example when a variable is defined by other variables that do not feature in the original equation. For example if you had:
$f(x,y) = 2x + 3y , x = x(r,w) , y = y(r,w)$, you could calculate the total derivatives of the function $f$ with respect to the independant variables $r,w$ rather than the partial derivatives of the dependent variables $x,y$.
Now, I want to know what the difference between that is and the total differentials, intuitively. I see that I can calculate the total differential of a function $f = f(x,y,z) = xy + 2yz + z -4z^{1/2} = 7$ as $f_x dx + f_y dy + f_z dz = 0$ whereby $f_x$ is the partial derivative of $f$ w.r.t $x$. But what is this 'total differential' actually telling me? Could someone verify my understandings and explain why/ when this total differential is used and why/when a total derivative is used? Many thanks.