According to the Department for the Regulation and Control of Magical Creatures, magical creatures are classified on a scale from 1 (X) to 5 (XXXXX) as followed:

• X: Boring
• XX: Harmless / may be domesticated
• XXX: Competent wizards should cope
• XXXX: Dangerous / requires specialist knowledge / skilled wizard may handle
• XXXXX: Known wizard killer / impossible to train or domesticate

SPOILER!!: Classified Creatures (X-XXX)

Classification X

• Flobberworm
• Flying Seahorse
• Horklump

Classification XX

• Augurey
• Bowtruckle
• Chizpurfle
• Clabbert
• Diricawl
• Fairy
• Ghoul
• Gnome
• Grindylow
• Imp
• Jobberknoll
• Mooncalf
• Owl
• Porlock
• Puffskein
• Ramora
• Winged horse

Classification XXX

• Ashwinder
• Billywig
• Bundimun
• Crup
• Doxy
• Dugbog
• Fire crab
• Fwooper
• Glumbumble
• Hippocampus
• Hippogriff
• Jarvey
• Knarl
• Kneazle
• Leprechaun
• Lobalug
• Mackled Malaclaw
• Moke
• Murtlap
• Niffler
• Nogtail
• Pixie
• Plimpy
• Pogrebin
• Red Cap
• Salamander
• Sea serpent
• Shrake
• Streeler
• Winged horse

SPOILER!!: Classified Creatures (XXXX-XXXXX)

Classification XXXX

• Centaur
• Demiguise
• Echinokarp
• Erkling
• Erumpent
• Forest Troll
• Golden Snidget
• Graphorn
• Griffin
• Kappa
• Kelpie
• Merpeople
• Mountain Troll
• Occamy
• Phoenix
• Re'em
• River Troll
• Runespoor
• Sphinx
• Tebo
• Thestral
• Troll
• Unicorn
• Winged horse
• Yeti

Classification XXXXX

• Acromantula
• Basilisk
• Chimaera
• Dragon
• Lethifold
• Manticore
• Nundu
• Quintaped
• Werewolf

Beasts versus Beings

According to Minister for Magic Grogan Stump in 1811 a Beast is loosely defined as "a magical creature that does not have sufficient intelligence to understand the laws of the magical community nor bear part of the responsibility in shaping those laws" while a Being does have sufficient intelligence to understand the for-mentioned laws.

Quote:

Originally Posted by Classified Beasts & Beings

Beasts

Acromantula* · Ashwinder · Augurey · Basilisk · Billywig · Bowtruckle · Bundimun · Centaur* · Chimaera · Chizpurfle · Clabbert · Crup · Demiguise · Diricawl · Doxy · Dragon · Dugbog · Echinokarp · Erkling · Erumpent · Fairy · Fire crab · Flobberworm · Flying Seahorse · Forest Troll · Fwooper · Ghoul · Glumbumble · Gnome · Golden Snidget · Graphorn · Griffin · Grindylow · Hippocampus · Hippogriff · Horklump · Imp · Jarvey · Jobberknoll · Knarl · Kappa · Kelpie · Kneazle · Leprechaun · Lethifold · Lobalug · Mackled Malaclaw · Manticore* · Merpeople* · Moke · Mooncalf · Mountain Troll · Murtlap · Niffler · Nogtail · Nundu · Occamy · Phoenix · Pixie · Plimpy · Pogrebin · Porlock · Puffskein · Quintaped · Ramora · Red Cap · Re'em · River Troll · Runespoor · Salamander · Sea serpent · Shrake · Sphinx · Streeler · Tebo · Thestral · Troll · Unicorn · Werewolf* · Winged horse · Yeti

Beings

Giant · Goblins · Hag · House-Elf · Human · Vampire · Veela · Werewolf*

* denotes an exception to the standard rules of classifying