Delta y is the difference between two values of y and so it's measurable finite number. dy on the other hand is just a marker for the infinitesimal change of y known as differential and used to denote derivates and integrals. So$\frac{ dy }{ dx }=\lim_{\Delta x \rightarrow 0}\frac{ \Delta y }{ \Delta x }$is the definition of derivative of y over x and$\int\limits_{}^{}\frac{ 1 }{ y }dy=\ln \left| y \right|+c$is the integral of y^-1 in respect of y.