Present continuous (I am doing) with a future meaning.
This is Ben’s calendar for next week.
He is playing tennis on Monday afternoon.
He is going to the dentist on Tuesday morning.
He is having dinner with Ann on Friday.
In all these example, Ben has already decided and arranged to do these things.
I’m doing something (tomorrow) = I have already decided and arranged to do it:
A : What are you doing Saturday night? (not What do you do)
B : I’m going to the theater. (not I go)
I’m not working tomorrow, so we can go out somewhere.
Sam isn’t playing football next Saturday. He hurt his leg.
“I’m going to (do)” is also possible in these sentences:
What are you going to do Saturday night?
But the present continuous is more natural for arrangements.
Do not use will to talk about what you have arranged to do:
What are you doing tonight? (not What will do)
Eric is getting married next month. (not will get)
You can also use the present continuous for an action just before you begin to do it.
This happens especially with verbs of movement (go / come / leave, etc.):
I’m tired. I’m going to bed now. Goodnight. (not I go to bed now)
“Tina, are you ready yet?” “Yes, I’m coming.” (not I come)
Simple present (I do) with a future meaning
You can use the simple present when you talk about schedules. programs, etc. (for public transportation, movies, etc.):
My flight leaves at 11:30, so I need to get to the airport by 10:00.
What time does the movie begin?
It’s Wednesday tomorrow. / Tomorrow is Wednesday.
You can use the simple present to talk about people if their plans are fixed like a schedule.
I start my new job on Monday.
What time do you finish work tomorrow?
But the continuous is more commonly used for personal arrangements:
What time are you meeting Ann tomorrow? (not do you meet)
What time are you arriving?
I’m going to the movie tonight.
What time does the plane arrive?