If son catches cold from school, gets sick, recovers, returns to school where cold virus still lingering, will he catch same cold virus again?

No, he should not: get the exact same cold virus, as he should develop protective antibodies, at least temporarily, to that virus. Unfortunately, there are so many strains of viruses that cause the common cold, that it is virtually impossible to be immune to them all. So, he could certainly get another cold right after the one from which he just recovered.