What's the difference between $f \cdot g$ and $f(g(x))$? For example if
$f(x) = x + 2$
and
$g(x) = 4x - 1$
Then what would be the difference in $f \cdot g$ and $f(g(x))$?

If dot means composition then they are the same. $$(f \cdot g)(x) = f(g(x))=(4x-1)+2=4x+1$$
If dot means multiplication then
$$(f \cdot g)(x)=(x+2)(4x-1)=4x^2+7x-2$$
