I'm afraid I don't understand your schema . . . are there other types? If there are other types, how are they represented in design #2?

There are only two "types". There are facts, and aliases. I don't really think of them as types, though. I think of them as completely different things. This is the crux of the difference between the two designs.

2 meaning that it's an alias and that the data should be interpreted as a fact_id

Yes, this is how Design 1 was intended to work.

Also, btw, both "name" and "type" are SQL reserved words and should not be used as column names unless they are quoted.

True. They were really just for the sake of the example.