Is this mold or a water leak, and do I need to call someone?

What people tried

Every workaround mentioned in the threads below. We haven’t tested any of them — and nobody here is claiming they worked.

1. 1
   Waiting to see if it drips
2. 2
   Inspecting the texture to see if it is just accumulated dust
3. 3
   Checking the basement for leaks
4. 4
   Turning off the water line during fall and turning it back on in spring
5. 5
   Opening up the drywall to inspect behind it
6. 6
   Cutting out the affected drywall and patching it

In their words

Unedited, grouped by where they were said, most upvoted first within each place, each linked to the thread it came from.