[subject] + am/is/are + [verb]-ing + [future time]
The present continuous can talk about the future when the plan is fixed: you have decided, you know when, and often someone else knows about it too. It's for the things you write in your diary.
A time word, or the situation, shows that it's the future. Without one, the same sentence is about now.
Both talk about plans. Use the present continuous for an arrangement with a time and often a place. Use going to for something you have decided, even when nothing is fixed yet.
Nobody arranges the weather, so use will or going to for it.
For timetables (trains, films, classes), use the present simple.