0-3 vs. 3 month clothing

I feel like clothing sizes for babies is so confusing!! Is 0-3 the same as 3 months?? I am thinking no because my LO is 9 weeks old 21 inches 9lbs 14 ounces and is just now fitting into 0-3 month clothing. I also have some 3 month clothing for her and it looks to big! We are coming up on the cold season and I really don't know what size to buy in warmer clothes. Carters sizes is either 3 months or 6 months nothing in between... What size should I buy?!?!