= Solution
A <version of a stochastic process> means a <stochastic process> on the same probability space such that, for every fixed $t$,
$$
\mathbb P(X_t=Y_t)=1.
$$
The exceptional <null set> may depend on $t$. <Indistinguishability of stochastic processes> means that there is one <null set> outside which $X_t=Y_t$ for all $t\geq0$ simultaneously.
For an example separating the definitions, let $U$ have <uniform distribution> on $(0,1)$, and set
$$
X_t=0,\qquad Y_t=\mathbf1_{\{t=U\}},\qquad t\geq0.
$$
For every fixed $t$, $\mathbb P(U=t)=0$, so $Y$ is a <version of a stochastic process> with original <stochastic process> $X$. But for every sample outcome the <stochastic processes> differ at its time $t=U$. Hence
$$
\boxed{\mathbb P(X_t=Y_t\text{ for every }t\geq0)=0.}
$$
The spike path of $Y$ is not <right-continuous> at $U$, which explains why the next part's regularity assumption rules out this example.
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