The four kingdoms of eukaryotes are:

• Animals
• Plants
• Fungi
• Protists

So, taxonomically, plants are as different from fungi as they are from animals.

Above that is the domains of life:

• Eukaryotes (all of the above)
• Bacteria
• Archaea

Then above that:

• Cellular life (all of the above)
• Viruses
• Viroids
• Obelisks (Potentially. Just announced last month.)