In biology, a kingdom is the second highest taxonomic rank, the first one being the domain.
The domain Eukaryota is traditionally divided in the kingdoms Plantae, Animalia, Fungi, and Protista; and consist of the following types of organisms:
Plantae: All plants, mostly photosynthetic, including mosses, ferns, gymnosperms, and flowering plants
Animalia: All animals, heterotrophs, and with a nervous system, including jellyfishes, insects, mammals, and many others.
Fungi: All organisms with chitin in their cell walls, including yeast, molds, and mushrooms.
Protozoa: Mostly unicellular organisms that cannot be placed in the other kingdoms.
Below I'll list the organisms with the kingdom to which they belong:
Cat - Animalia
Frog - Animalia
Mushroom - Fungi
Grass - Plantae
Worm - Animalia
Shark - Animalia
Mold - Fungi
Bacteria - Domain Bacteria
Apple Tree - Plantae
Fern - Plantae
Rose bush - Plantae
Corn plant- Plantae
Of the four groups of organisms, just the members of the last one belong to the same kingdom.