覆う and 包囲: covering a surface and surrounding a target
Compare covering a dish with a cloth and surrounding a castle in a story. Read the purpose of the covering and the directions of the encirclement.
覆う: covering the dish
覆う（おおう） means to cover. 「料理が冷めないよう布で器を覆う。」 describes covering a dish with a cloth so that the food does not cool. 器 is the object being covered, and 布 is the material used.
Keeping the food from cooling is the purpose of the action. 覆う is nonpast here, so the sentence should not be turned into a report that the covering was already completed. It does not state whether the food actually stayed warm or whether every gap was closed.
包囲: surrounding the castle
包囲（ほうい） means encirclement or siege. 「物語では城が四方から包囲された。」 reports that, in the story, the castle was surrounded on all sides. The focus is on the directions around the castle, and 包囲された is a past passive form.
四方から means from all sides. The sentence identifies neither who surrounded the castle nor what was happening inside it. Surrounding its perimeter does not mean covering its surface like a cloth or making the castle disappear from view.
Follow the spatial relationship
The dish and the castle are the respective targets of the actions. The 覆う example describes a cloth covering the dish; the 包囲 example describes encirclement around the castle. Following the covered surface and the surrounding perimeter helps distinguish the relationships.
The purpose of keeping food warm and the direction from all sides add different kinds of information. Neither establishes a complete seal or the possibility of escape from the castle. Keep the interpretation within the covering and encirclement described.
Does the castle's 包囲 describe covering its surface, as 覆う does in the dish example?
Show the answer and why
No. The castle example describes encirclement from all sides. This differs from the covered surface in the dish example. Encirclement alone does not establish that the castle's surface was covered or that the castle was hidden from view.