Days survived is time from zero hour (five days post-cataclysm) to your death.
Days adventured is the days you were actually playing, if you were on a delayed start.
Since opting to start later than Spring doesn’t delay the cataclysm and therefore is generally a tougher start (perishables perish and wildlife gets zombified, foraging shifts, etc), it’s important to make a note of that fact.
Conversely scorekeepers and such might get all discombobulated if we counted days that were fast-forwarded (wherein you passively Stay Alive but don’t develop and are not at risk) the same as days actively played, where hunger/thirst/etc are issues and you have to look after yourself.
So, compromise, and two trackers.