My son, 20 weeks old, has had loose stool for 2 weeks and tested positive for c diff. The nurse said he could be a carrier. Is that typical?

No, but not rare. It's not typical, but it does happen from time to time.
Yes. C diff is very often present in the GI tract of infants and children less than 2 years old. It is not considered to be a pathogen (a disease causer) in these situations, and I am fairly surprised they even tested your son for it. It is unlikely to be the cause of your sons diarrhea in my opinion.