I must respectfully disagree: both are evidence. The "person telling you" is anecdotal evidence; "what they saw" is observational evidence (for them).
Yes, I have said that. It gets lost in the semantics. One is evidence the person is telling you about. But the person telling you, if you are going to now call that the evidence, is something altogether different from the evidence they are describing. And that is the key difference.
There is the evidence the person drew their conclusion from.
There is the anecdote the person is telling.
Those are not one in the same. And if you are going to say there is evidence of fairies, there is a difference between those two actual evidences. One is evidence, but that is not what we have. One is a conclusion. It is evidence the person believes something. But it is not evidence of the thing they believe. At least not in the case of fairies.
...I think the problem is that "evidence" has more than one meaning, and that meaning is context dependent. When the meaning in one context is mistakenly employed in another context, then people talk at cross-purposes.
The meaning is less of the problem than what one is referring to when using the term.
The anecdote is evidence. Referring to the anecdote, one must be careful when distinguishing between observational evidence which has evidence one can review, it exists, it can be observed by others; and, anecdotal evidence, which is still evidence, but there is no thing one can also observe to confirm the observation, no one else could have observed the evidence at the time it occurred. That evidence is then the person telling you something. It is the person's conclusion. It is evidence of what the person believes, but it is not evidence of an observation unless there actually was a physical observation made of something. The difference is between the thing observed and the observation itself.
..The nature of the information which constitutes the evidence doesn't change, but the interpretation of what it is evidence of or for certainly does.
Exactly. Believing or drawing a conclusion about something does not make that thing evidence of the belief or conclusion. It has to actually be evidence of that belief or conclusion. Just believing does not create evidence which did not exist in the first place.