Do both mean the same: Tell me how many people are going/coming.
What's the difference?
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The difference is the point of view of the person speaking. If the speaker intends to be at the event, they will probably say "how many people are coming?" If the speaker is not involved, they will say "how many are going?"
Note: this is an deliberate use of "singular 'they' " -- used in place of "her or she" or the default "he."