No, ag zoning refers to the actually zoning category like residential, commercial, agricultural, transitional. “Green belt” refers to how a property is categorized for taxes purposes.
Another thing to keep in mind is please do not believe what anyone tells you about zoning, green belt status or even if a property can have horses on it. Just because there is acreage, does not mean there are not restrictions on if you can have horses there, how many you can have, and how you can house them. Never make any assumptions- always go to the zoning office yourself and do your own research. Do not even believe your own real estate agent.