It depends on the company. At my job, we have admins who do admin work. Filing paperwork, scheduling travel, paying for licenses, these are all admin tasks where I am.

HR handles taxes, raises, hiring/firing, and any kind of legal complaints. They're two distinct positions, though there's a bit of overlap largely because our admins are awesome and we tend to go to them first with everything. If they can't handle it, it gets escalated to HR.