What is the difference between dy/dx and d/dx in Calculus?

What is the difference between $\frac{dy}{dx}$ and $\frac{d}{dx}$ in Calculus?

In Calculus, when we write $\frac{dy}{dx}$, it means we are differentiating the function $y$ with respect to its variable $x$. For example if $y=3x^2$ then to find $\frac{dy}{dx}$ means we will be differentiating $y$ but by paying attention to only the variable $x$ which yields $\frac{dy}{dx}=6x$, even if a function has multiple variables say $y=3x^2+2y-3z$ and we are to find $\frac{dy}{dx}$, it means our differentiation will only pay attention to the variable $x$, ignoring the other variables $y$ and $z$, this is the genesis of partial differentiation.

But when we write $\frac{d()}{dx}$ it means we are to differentiate the $x$'s in the brackets. For example $y=\frac{d(x^2-3)}{dx}=2x$ same thing applies to $x=\frac{d(t^5-2t^2+1)}{dt}=5t^4-4t$