I don't think there's one at either. Security concerns means that these are now quite rare since they need airport-style security (baggage scanners etc) to operate, which makes them to expensive to run except at a few locations.
According to SNCF, there is no luggage storage at the train station. See https:/…services
In France, a "bus terminal" is usually some bus stops at the side of the road. So far as I can see from Google Maps, this is the case in Annecy.
there is no luggage storage at the train or bus station...
but I think that some people go for a drink/meal at a restaurant/bar next to the train station and kindly ask them to keep their luggage, nothing official but seems ok
The bus and train station are side by side at the same location. There are not any left luggage lockers - but a couple of years ago one of our apartment guests found a vegetable shop opposite the station who provided a left luggage service for 3 euros per hour. I don't know if they still provide this, but he discovered it by asking at the information place in the station.
I was in Annecy yesterday and can confirm - there is grocery store Vival abit almost afront a train/bus station, abit to right. Address is
1 Rue de l'Industrie
They've stored my bag for 3 Eur/h.