Is how much we sweat an indicator of how much calories we burn? I am talking about the same person because how much we sweat is also related to how much the body is hydrated.
As Eric put it, sweat happens when your body needs to lower its temperature.
Sweating is not necessarily a good indicator of how many calories we burn, it is tied to it to some degree though.
People will often tell you that when you break a good sweat during workout, you did just fine! But the truth is that you can sweat quite a bit in sauna, and after you get out and drink some water, you will be back to your previous weight state.
If you are curious about how we lose fat, there is an excellent TED video that explains it: https://www.youtube.com/watch?v=vuIlsN32WaE
The bottom line of the video is, fat is expelled by breathing. So a better indicator of if you are burning calories or not is how fast are you breathing.
We sweat when our body has excess heat that it can't get rid of.
If you are exercising in cold weather, your body can easily dump excess heat into the cold environment. If it's hot, however, it can't do that, so it tries to dump heat through sweating and having the water evaporate, removing heat from your body.
Sweating as also a trained reaction; athletes who are better trained will sweat more.
If you do two workouts in a room of the same temperature wearing equivalent clothes, if you sweat more you are probably working harder at that point.