The interruption under section 99 StVG concerns ongoing enforcement, the postponement under section 6 StVG the time before commencement.
Both instruments defer enforcement but apply at different points. The postponement under section 6 StVG comes into consideration before the sentence has commenced, for instance on important personal or economic grounds. The interruption under section 99 StVG, by contrast, concerns a prison sentence already commenced and pauses ongoing enforcement. Anyone not yet in custody therefore first considers the postponement; anyone already serving, the interruption.
What to do now: First, clarify whether the sentence has already commenced, because this determines the right route. Second, name the occasion; urgent personal, economic or health grounds come into consideration. Third, bear in mind that the interruption is a discretionary decision and not automatic.