James has indicated there is a difference. I will simply add that in difficult circumstances some people try to remain cheerful. It would be very odd for them to remain 'jolly.' That would suggest they are almost in a party mood!

I would not use "jolly" unless you are confident you know what it means. It gives many people a mental image of a chubby guy with red cheeks who giggles, like Santa Claus. I think many people would be insulted if you called them jolly.

There is no difference. Both words have the same meaning.