Nutshell, what's the National Curriculum Attainment Target on about when it contrasts "information" and "evidence"? Aren't they the same thing?

They aren't really things. The contrast is between ways of thinking about knowledge rather than between things.

Pardon me?

One way of talking about knowledge involves ‘looking things up': we assume that the answers to our questions are already known and that all we need to do is find out who knows them and look them up. Another way of thinking about knowledge involves ‘working things out': if you work it out you don't look it up and it is quite possible that ‘it' did not exist until you worked it out. The first way of thinking models knowledge as information finding and the second as problem solving; the first is about finding the answer somewhere and the second about making the answer somehow.