Pitcher after a rain delay

[Jay R]

OBR, regarding rule 4.12(c).

This rule states that if a relief pitcher has started to warm up and there is a rain delay before he pitches to a batter or retires someone, he does not have to pitch when the game is "later resumed".

I want to verify how do we interpret "later resumed"? The game resumes 30 minutes later or the game resumes two weeks later. Would there be a difference?

Thank you.