It is a piano technique question.
How to play technically right D(Eighth note) and C(Half note)? Start together or C goes after a little delay? (in the first measure).
The same for the accord E+G and D in the second measure.
All of these note pairs have to played simultaneously. The horizontal offset is just added to avoid printing note heads over each other. (As a rule, when notes sound after another, the heads will be farther apart than this - at the very least they would be no horizontal overlap.)