Does spacetime comprises of any smallest “frames” units? E.g. Planck units?

If so, how is it compatible with relativity? I.e. consider e.g. the twins “paradox” in which twin B returned younger than twin A, meaning after each Planck time unit – or any other natural unit contender – a smaller time unit passes for the other twin. Same goes for an atomic clocks, when clock A ticks 1 Planck unit, what did clock B ticked relative to it?

Asked Adam

Since it converges to zero, is it falty to conclude that spacetime is continuous?

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