A winery is where you make wine. It is typically thought of as the production facility. Most people would say it also includes the tasting room, restaurant, conference rooms and any other buildings that are also on the premises.
The Vineyard is the farm field where you grow the grapes.
When you visit a winery, they are typically a winery and a vineyard as they produce wine and grow grapes. There are many more vineyards than there are wineries as most wineries will have multiple grape producers.
However, there are instances where a winery does not have a vineyard, in particular if it is a fruit winery. It would therefore be making wine with fruits other than grapes. These instances would be few however, as the vast majority of wineries make wine with grapes.