Four names around here, and the wrong name wastes a phone call
Grayson County issues a zoning permit on its own numbered form, for land outside its three incorporated towns. Montgomery County, Virginia routes the same question through a zoning verification letter, off a Request for Zoning Review form, and publishes on its own page that approvals are generally done within 1 to 2 business days of submittal. The City of Galax publishes a Zoning Permit Application and a Certificate of Zoning Compliance Permit. Wilkes County, North Carolina folds it into a Watershed or Zoning permit from its Planning Department, phone 336-651-7563 or 336-651-7582, and sends lots inside a town or its extraterritorial area to the Town of Wilkesboro or the Town of North Wilkesboro.
Four jurisdictions, four sets of names for closely related paperwork. All of them are a planning body writing down that the thing you described is allowed on that ground. None of them is a statement about concrete, thickness, base or steel, and none of them is issued by a building official.
Call it whatever the jurisdiction calls it, and ask by the name printed on its own form. The question does not change because the word does, and the word is the only part of it a homeowner can get wrong before the conversation even starts.
Where it stands in front of the building permit
In Grayson County the planning side goes first, and the county says so in its own submission sheet. That sheet lists seven things to bring before a building permit will issue, numbered one through eight because item four was skipped, and the zoning permit sits at number two. Which office issues that one depends on where the lot sits. Out in the county it is the county's zoning administrator. Inside the Towns of Independence, Fries and Troutdale the towns administer their own zoning, so zoning goes to the town office even though the building permit still comes from the county. The building permit will not issue without the zoning step.
Wilkes County starts a homeowner at the same kind of counter, sending them to the Planning Department for the watershed or zoning permit and the flood damage prevention paperwork before anything else happens.
That order of operations is the practical value of knowing this word. A building department in a zoned jurisdiction may decline to take your application at all until the planning office has signed, and discovering that on the morning you wanted concrete delivered is an expensive way to learn it. Ask which order your jurisdiction works in at the same time you ask what its building department needs.
In some jurisdictions here there is nothing to apply for
Zoning is optional in both states. A locality may adopt an ordinance and a locality may decline to, and a county without one has no districts, no zoning administrator signing things and no permit of this kind to issue. That is not a loophole and it is not rare in this corner of the two states.
The line that decides it is frequently a municipal boundary rather than a county boundary. Carroll County has no county-wide zoning ordinance and the Town of Hillsville, sitting inside it, has a full zoning chapter of its own. Grayson, which shares a line with Carroll, zones countywide. Surry County's zoning stops at the incorporated areas of Dobson, Elkin, Mount Airy and Pilot Mountain and at the extraterritorial jurisdictions attached to those towns, where the county ordinance says outright that it does not apply, apart from one provision on wireless communication towers inside Elkin's planning jurisdiction.
None of that is permanent. Counties draft ordinances, table them and revisit them, so anything you read about a jurisdiction's zoning status, on this page included, is only as good as the day it was read. Ring the county or the town and ask. It is a free call and it takes one question. The towns we work in do not all answer it the same way.
What this sign-off does not settle
It has no view on how the concrete is built. Thickness, base, reinforcement and inspections sit on the building code side of the counter with a different office and a different set of documents behind it. It does not clear the strip out at a state maintained road either, which answers to the state transportation department and needs permission of its own. And it says nothing about a recorded easement crossing the lot, because that right came out of a deed rather than out of any county ordinance.
Where zoning is absent, the absence removes one authority and leaves every other one standing. Land disturbance thresholds, floodplain rules, subdivision restrictions, the building code and the road are all still in play, each with its own desk and its own paperwork.