If you have stucco walls and are unsure whether they are traditional or synthetic, it’s no surprise. They two look almost identical. The easiest way to see is to simply push on the wall. Traditional stucco will be rigid, while the synthetic will be a bit softer.
Also, if there is an opening in the wall like a light fixture, vent, or other hole in the wall (hopefully not made by accident or a handyman’s unfinished work), you will be able to see the layering. If there is wire mesh under the stucco, it is traditional stucco, if there is a layer of foam, it is synthetic stucco.