"Estar/Ir de compras" would be more like a pleasure. Enjoying when you go to buy clothes or similar. "Ir a comprar" is more related to do groceries, for example. Not for pleasure but because of a need.

Leo 你好! "Está de compras" ( in this sentence the subject is omitted: el/ella // he/she ) = means " (He/she) is shopping" "Está comprando" means the action of the verb is happening right now, the subject is buying something in this moment. It's similar to 正在 in chinese. Other example: "(el/ella) está de paseo" and "(el/ella) está paseando" Best wishes Sofía