The present continuous.

1.My boss is traveling to Australia next month to open a new business.

At this sentence, is traveling which means is already in Australia or is still in preparation in original place(not arrive in Australia yet or is not on the way to Australia).

2.Peter is playing basketball in the schoolyard.

Apparently, Peter is in doing something(playing basketball) and in the schoolyard.

Compared sentence 1 with sentence 2, I can’t tell the sentence 1.

The first sentence suggests that your boss has planned on travelling to Australia next month. It’s just a plan. He hasn’t started travelling yet.

You can use present continuous tense when speaking of plans you have made for future. See examples below.

  1. I am going to buy a car next week.
  2. She is getting married next month.

The second sentence suggests that the activity is going on now, right at this moment.

You can use present continuous tense this way, too.

Very clear,Daemon, thanks for explanations in detail.

So (be V-ing) can still be a idea in the future.

Originally, I thought (be going to V) is the only expression, now I see, thank you.

This is about an arrangement made in the past about the future, because we have “next month”. You know for certain that your boss will be in Australia next month, and so you can be late for work without any repercussions.

This is kind of ambiguous.
It may mean that now he’s playing, or that he will be playing at some time later. Broader context will dispell any ambiguity regarding this.

For example:
Peter’s mom: Peter won’t be playing with you because he’s got tons of homework to wade through
Peter’s friend: No way, Peter is playing basketball in the schoolyard with me, period! I don’t care what you think! (very impertient)

Peter’s mom: Where’s Peters? (inquiring about Peter’s whereabouts)
Peter’s friend: Peter is playing basketball in the schoolyard.

I see, it still depends on situations, especially who talkers’ point at and who the subject is.

Thanks Our Tort System.