The first is more precise. If someone tells me they will be here in 20 minutes, I expect them no later than 20 minutes. They would be late after 20 minutes.
The second is an undefined amount of time. That is, they may come at 25 minutes, 30 minutes, etc. Essentially , they’re saying it will take them at least 20 to get there, but they don’t know how much longer.
If you want to give a range, it would be: I will be there between 20-30 minutes.
BTW, another way to say #2 is: it will take me at least 20 minutes to get there.