Use exquisite to mean finely or delicately made or done. When you say someone has exquisite taste, you mean that they are able to make fine distinctions.
Exquisite describes something that is lovely, beautiful, or excellent. Exquisite pain or agony is very sharp and intense. Exquisite is from Middle English exquisit, from Latin exquisitus, from exquirere “to search out.”
of extreme beauty“her
delighting the senses or exciting intellectual or emotional admiration
lavishly elegant and refined
intense or sharp