A whale (고래, gorae) inherits the ocean's general association with scale and takes it to its natural extreme — whatever a whale dream is about, it's read as considerably bigger than an ordinary fish dream, simply because the animal itself is enormous.
Riding a whale, or watching one breach the surface clearly, is read as achieving or witnessing success on a genuinely grand scale — an ambition realized at a size that goes beyond ordinary, day-to-day fortune. A whale surfacing after being hidden underwater is read specifically as a big opportunity finally becoming visible after building quietly out of sight.
Being swallowed by a whale is one of the more dramatic variants in this entire tradition, and echoes a very similar motif found well beyond Korea — being taken in by something overwhelming, only to eventually emerge changed, is a near-universal story shape. The dream is generally read the same way: a temporary, overwhelming setback that you come through rather than one that ends things.
A calm, distant whale simply passing by, without direct interaction, is read more mildly — awareness of something large-scale happening nearby (in your industry, your family, your community) that doesn't directly involve you yet.