While there are yarns that say "Baby" on the label, there really is no such thing as a "Baby" yarn.  "Baby" yarns range in size from Fingering up thru Aran weight.  Some baby yarns are 100% cotton (or a blend), others are 100% Merino wool (or a blend).  And yes, babies all over the world are kept warm and cozy in homemade woolens.  Wool is the perfect fiber that stays warm even when wet.  It also breathes, helping to prevent the baby from overheating. 

These yarns are ones that are particularly well suited for baby items.  They are all machine washable. They are all wonderfully soft.