Birds transport fish eggs from other ponds on there feet and belly, my friend has a pond full of bass and bluegills, but he never stocked it the geese did it. Crawfish will travel and turtles definately do, when i lived in ohio I always carried my 22 in my car cause people were always asking me to dispose of giant 3' snappers that would be in there yard, porch, pond, etc. If you found one in your front yard than you most likely have one/some in your pond and they can be dangerous if you let small children swim in your pond, I saw a goose disapear in our pond before I found the giant culpret and put him down. They also carry lots and lots of parasites. So be aware of the snappers and check that pond every so often, those "minnows" could be baby bass and if not you might get some soon so can I come over and go fishing?
Koi are a tipe of carp like stated before and get verrrrrryyyy large, I'm serprised so many of you have never seen a koi pond before with fish from 2 - 4 feet long. The ones in the pictures are pretty average size they can get a lot bigger.