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  1. I don't understand why the phrase "we are seeing them tonight" is correct. I would rather say "we are going to see them tonight" because the construction "to be going to" is used when you have planned something and will do that anyway. But here is a real Present Continuous with state verb "to see" used to show planned actions in future, but as I know it's not correct state verbs with Present Continuous Tense.

  2. Are the phrases "we are seeing them tonight" and "we are going to see them tonight" equal and have the same meaning?

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To see is not always a state verb. In the sense of visit, meet, or have a relationship with it is not stative.

The present continuous can be used to express future plans.

"I'm meeting her tomorrow."
"We're playing football next week."

The British Council has some good summaries regarding talking about the future.

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