It may seem strange to think that wine should be Vegetarian or not. The reason for the difference surrounds the chemicals commonly used in winemaking and primarily, the process of clarifying and stabilising the liquid before it goes into bottles. This process stops the wine from losing its colour & developing unwanted aromas. Products typically used are isinglass (a product that comes from fish bladders), gelatine and then dairy products casein (milk protein) and albumen (egg whites). The latter two are generally accepted by Vegetarians and wine labelled as vegetarian can contain these two. However neither are of course acceptable in Vegan wine.
What’s the substitute? Now Vegan friendly options are often used, these include bentonite but also activated charcoal which is often used in the process of filtering water.
Of course, if none of the above sounds appealing, you can always aim for a Natural wine where most often, no clarifying or Stabilisation takes place.