When you make someone’s acquaintance, you meet them for the first time and get to know them a little.
If you have an acquaintance with someone, you have met them and you know them.
[C] a person that you know but who is not a close friend 认识的人；泛泛之交；熟人
Claire has a wide circle of friends and acquaintances.
克莱尔交游很广。
He’s just a business acquaintance.
他只是业务上认识的人。