Well, here's how it would be:
The numbered classes (1-5...six would no longer be necessary) would classify the actual abilities.
The descriptive classes that I have listed would describe the Variant themself. These are used as a codeword to get a quick read on a Variant's capabilities with as few words as possible.
With what you have,
@Ceta de Cloyes, you're only classifying abilities. If I were to just tell you there was a 'Red level Variant with enhancements' that you needed to deal with, you would have no idea what to prepare for. However, if I instead told you that there was a 'Red level Brute', you would be expecting someone with super strength and not someone who can blow you up. That's the point of the types.
The types basically describe how a Variant would be perceived upon someone first meeting them and seeing their powers in action. Some Variants might fit into multiple categories by default...for example, Nightwolf could possibility be a Brute, Agile, Amplifier, and/or Metamorphic, but only the Metamorphic descriptor would be necessary because it describes how his abilities are mainly used. The rest are basically side effects.
Edit: Like this...
Sabrecat -- Metamorphic
Allomancer -- Architect
Scavenger -- Metamorphic
Roach -- Amplifier
Sway -- Mentalist
Dynamo -- Metamorphic/Architect
Gizmo -- Metamorphic
Tank -- Brute
Don -- Amplifier/Natural
Aria -- Amplifier
Titan -- Amplifier
Identia -- Architect
Shadowbroker -- Distortionist
Nightwolf -- Metamorphic
Jayson -- Mentalist
These describe the overall view without trying to nitpick their powers apart and describe each one. Make sense?
Blazion