I have a weather app I made for photographers and working on putting a drone forecast in it. So let me take a guess because I'm a little knowledgeable in it.
To me, looking at both photos, it seems about 2 hours apart?
Forecast is not totally likely to change a whole lot in 2 hours, but it can happen, especially as more weather data comes in from the sources. I believe Dark Sky is the weather data service UAV forecast probably uses (I do as well) and although they don't provide info on where they collect the weather data from, it's most likely a mix of observational and forecasted data from local weather services, NOAA, and observational data from airports. As time goes on, more accurate data may be available and they may switch their sources to provide a more accurate forecast.
As far as sunrise/sunset time discrepancy, it can be a few things:
1. Your GPS signal was a bit off and it had you at a location further away, and it affected the sunset time enough to meet the threshold to consider it 1 minute, even if it was only a few hundred meters off.
2. There may have been a connection issue contacting the server and they may have a failsafe built into the app to calculate sunrise and sunset time even when you have no internet connection. This is easy to do with mathematical formulas but for some reason I've seen different results by 1 minute too.
3. Going off number two, there may have only been a problem connecting to tge dark sky server (they provide sunrise/sunset) and maybe it connected to the TimeAndDate.com server instead as a failsafe, I have also seen their numbers differ between both services for whatever reason.