Milk protocol

If I took breastmilk from the fridge and tried to feed it to baby and he didn't drink all of it, do I have to throw it out? Wasn't sure if it was like formula and once it's been drank from, has to be gotten rid of? I didn't heat it up in any way, just let it warm a little at room temp.

Also if I pump and plan on using it the same day, does it make more sense to just leave it at room temp or refrigerate?