What is the relationship between the discrete time and continuous time variables?
It's about the relationship between the discrete time signal $x_d[n]$ and the continuous-time signal $x_c(t)$:

$$x_d[n]=x_c(nT)\tag{1}$$

So you formally replace the variable $t$ by $nT$ but this just means that you sample the continuous-time signal at sample instants $t_n=nT$. So $t=nT$ is only true for the values of $t$ that we're interested in, and these are the discrete values $t_n=nT$.