These two sentences have the same meaning. For the future tense text books teach students to say I AM GOING TO PLAY BASKETBALL NEXT WEEK. But many native speakers simply say I AM PLAYING BASKETBALL NEXT WEEK. The difference is that the speaker omits the GOING TO and uses the -ING form of the sentence verb instead. This can be confusing because the structure of this future tense is the same as the present continous tense. The difference is thus understood from context or with the help of adverbs/adverbial phrases such as TOMORROW, NEXT WEEK, ON TUESDAY and so on.

It doesn't have to do with complete actions. Remember that the future is a hypothetical place, so in English we "construct" a future meaning. "What are you doing tomorrow?" - this asks about what arrangements you already have for tomorrow. It's present continuous with a future time. Pretty simple. "What are you going to do tomorrow?" - yes, this asks about a current plan. The "to be going to (action)" is used when you have evidence from the present which indicates the future action. In this example, you can use either but be aware these future forms cannot always be changed over. For example, "It is going to rain tomorrow" makes sense if you are now observing weather conditions that indicate rain later. However, "It is raining tomorrow" doesn't makes any sense.

i think 'what are you going to do tomorrow" is right.

There are three ways to talk about the future: will ______ be going to ____ ____ing They have the same meaning: I'll visit my doctor next week. I'm going to visit my doctor next week. I'm visiting my doctor next week. How about this one? I'm visiting my doctor. It could be right now, or it could be the future. In conversation, the meaning will be clear. I ask my friend "Hey, what are you doing next week?" He says, "I'm going to take the kids hiking." I say, "Oh, cool. Where are you going?" He says, "We're camping in Big Bear."

I think it's a matter of usage rather than meaning. The two questions are interchangeable and the usage may vary from place to place. I often use the ''going to...'' construction in everyday speech. Many italki questions asking about differences in meaning actually are referring to differences in usage.