Yes I’ve been to both, as @timb says they are quite distinct.
The Jura runs along the whole length of lake Geneva to the North. High Jura is near Geneva with smaller mountains & hills further East. I’ve done a bit of mtb riding and hiking in the Jura, its more xc generally with uplift and trails in Metabief. Quite rural as you would expect, famous for it’s Comte Cheese and the wine (vin jaune) good for mushrooms too. Quite varied from West to East. If you are going to be in the area its worth having a lunch on Lake Geneva perhaps in a town like Nyon (I have a friend who lives there) or taking a boat trip over to the French side to a town such as Yvoire (medieval well preserved, nice restaurant there near the water)
Annecy is a very cute town, can be busy with tourists though. Its worth making the effort to go on market days. Watersports on the lake. Good road riding around there and nice restaurants up in La Clusaz ski resort and also some mtb trails options which I’d like to explore more.