As you mention, I don't think the classification should work with tags, I was thinking more of a specific drop-down for this purpose. Of course we can accomplish this with tags too but a lot of things can be done with tags that the feature is getting a bit overcrowded.
A possible solution for this (and other use cases) would be the ability to create custom fields with predefined values that only administrators can set. Then we would be able to create custom fields for this and other stuff we want to categorize experiments into.