Hello, I have had aquariums for more than 40 years. I have had an outdoor koi pond for 20 years. I have about 9 or 10 koi and 2 goldfish in the pond. Its between 500-600 gallons. This summer I noticed about 15 baby fish swimming around. Some of my koi are more than 12 inches and my pond will not support 15 more. So I started to catch them and put them in my 55 gallon aquarium. Trouble is, I don't know what they are. Some are yellow and shaped like a koi but no barbels. Some are multi colored. None are short and stubby like a goldfish. Most puzzeling are the larger black, silver & gray ones. Carp, goldfish & koi are all related but could these possibly be your basic common carp? They do not have the "sucker" mouth. If there is a way I might get a photo and post it. Any ideas?
Welcome back to the forum! I could maybe tell you more with a photo. In general, goldfish breed more often than koi. Koi will have the barbels under their mouth. Both start out as black/gray/brown and then develop color. Koi usually develop color faster. Fish can also come from outside your pond. For example, as eggs brought in by a new plant, or as fish or eggs dropped by a passing predator. Koi and goldfish can also produce offspring although it is not very common, and they are sterile. These hybrids can look like koi and/or goldfish.
As far as crowding goes, the rule of 1000 gallons for the first koi and 100 gallons for each additional makes the most sense to me. Since your adult koi are only a foot long, they are only a few years old? If the babies are koi, you are certainly right that there's not enough room for them. There's also not enough room for more goldfish either. Either find them a home or start digging!