Definition of sampling using delta or indicator function?
that equation following "Conceptual scheme" is misleading.  the $\implies$ arrow is not an equal sign.  this is what is true:

$$\begin{align}
x(t) \times \sum\limits_{n=-\infty}^{\infty}\delta(t-nT_s) &amp;= \sum\limits_{n=-\infty}^{\infty}x(t)\times\delta(t-nT_s) \\
&amp;= \sum\limits_{n=-\infty}^{\infty}x(nT_s)\times\delta(t-nT_s) \\
&amp;= \sum\limits_{n=-\infty}^{\infty}x[n]\times\delta(t-nT_s) \\
\end{align}$$

because we simply define $x[n] \triangleq x(nT_s)$.

the difference between the dirac delta and the indicator function is that one integrates to an area of 1 and the other integrates to an area of 0.