Difference being between rest periods, and how may hours you were scheduled to fly in a 24 hour period. 8 hours scheduled flight time between rest periods means that duty day, whenever that duty day starts.
The 8 hour and associated rest times have to deal with scheduled flight time that took place in a 24 hour period. As we all know, 24 hour duty period can easily encompass 2 duty periods where you're scheduled to fly well over 8 hours in that 24 hours, but two separate duty periods.
Just going on rest times, and NOT reduced rest language. Scheduled less than 8 hours of flight time in a 24 hour period requires 9 hours rest.
If you were scheduled between 8 and 9 hours of flight time in a 24 hour period, but in 2 separate duty periods, you need 10 hours of rest, etc