I think there are SOME instances where it’s important to differentiate. If a doctor needs to know if baby is on breast milk or formula, then it doesn’t matter. But feeding by bottle- breast or formula milk- can lead to overfeeding more easily than breastfeeding from the breast can. There are also other things like your baby’s saliva can communicate to your breast when it’s sick and your body will adjust the milk for baby, etc. But that’s not anyone’s business