Suppose there is a distribution $D$.
$x$ is extracted directly from $D$.
$s = (a_1,a_2,\dots,a_n)$ is $n$ samples i.i.d from $D$.
then extract a sample $y$ from $s$.
Can $y$ be interpreted as being extracted directly from $D$?
I mean, $x$ and $y$ have same meaning?
Yes. It matters not how many sample you generate.
Since each set of samples in $(a_k)_{1\leq k\leq n}$ is selected independently and identically from $D$ (ie with replacement after each sampling), therefore it does not matter which sample you select $y$ from, it has the same probability of having a particular identity as if you had selected it dirrectly from from $D$.
Take a standard deck of 52 cards. Draw a hand of five cards, record it as $a_1$, replace it, shuffle and draw another, recording it as $a_2$, and so forth. Among $n$ such drawings you pick an index from 1 to $n$ without bias, then select one of the cards in that indexed hand. The probability that that card is the ace of clubs is: $1/52$, exactly as if you had drawn a single card straight from the deck.