I bought some 3/8" soft copper tubing, which fits the 3/8" compression
fittings just fine.

I also bought some 3/8" sweat elbows and Ts. They are way too big.

Presumably it is a matter of ID and OD being used for different components?
What size sweat fitting go with 3/8" soft copper?
What are the 3/8" sweat fittings for? I've never seen 3/8" hard copper.