Are my baby fish goldfish or koi?

Definitely Koi, there are a little young but still can breed at that age. In my experience with gold fish there never did breed and with Koi I had one but never knew till the gold fish died and it got big and put it in a pond. If there fat silver like minnows then there Koi but if there are birds that land in the pond or its near a lake it might be another species from that carried in by the birds, wait a few month or weeks to see what they grow to be.