From the Twitch FAQ:
Q: Why are my Sub Anniversary and Sub Renewal dates sometimes different?
A: Because we are shifting to a model that counts the actual days you’re subbed, any previous gap that we are bridging at launch potentially will add extra days to your subscription tenure. Don’t worry though, you’ll be able to share a resub message whenever you reach your sub anniversary if you are still subscribed.
My thoughts:
The anniversary date should always stay the same, depending on your first sub day, to synchronize it with sub badge changes.
Whenever a prime sub is activated, this is the “sub renewal date” and Twitch triggers the “new sub alert” in chat.
This is also the case when someone in manually starts a paid sub after the last one ended.
That’s why subscribers with autmatically renewing subs won’t get those new sub messages and just share their resub on the anniversary.