Those eggs both look like duck eggs; both color and texture seem alike. And it's not unheard of for birds, especially young ones, to lay two eggs in a day. My late goose once laid two eggs within one hour. If you want to be completely sure about the origin of the larger egg, crack it. Goose egg...
Just to clear up any potential confusion: Female birds lay eggs regardless of male presence.
Eggs from the same bird can vary very much in size. But duck and goose eggs have different textures and colors. Duck eggs have a more waxy surface and tend to be tinted bluish/greenish; whereas goose...