We don't have the budget

The use of the term can vary a lot depending on the context. In this situation, it is likely that the Atlanta-based company hired/contracted with a person/company to find suitable employees for their opening in data analysis. These “head hunters” are very good at seeking out employees like OP who may be appropriate for the position based on knowledge and connections in the industry. They are given the power to offer (often quite good) job offers as a way to more quickly fill the position.

So to answer your original question, yes and yes. They seek you out and help you look for a job- the catch being it’s a singular job and they aren’t working for you they’re working for that job’s company.

You can see this at a more casual scale with companies like Zip Recruiter that advertise on podcasts and things.

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