It seems like these are talking about the same issue, except possibly the concepts arose separately to describe how each work in different languages (maybe a bad analogy is genitive and possessive in Russian and English-- same core thing, but different terminology because they don't work identically)
Irrealis mood is used to talk about events that are not-real (ir-realis), such as:
If I had eaten an apple earlier I wouldn't be hungry now.
The condition (I ate an apple earlier) cannot be fulfilled any more at the time of speaking, or cannot be fulfilled at any time (If the Sun revolved around the Earth...)
Evidentials mark the source of information. English doesn't have grammaticalised evidentiality, but there are lexical expressions such as:
Rumour has it...
I'm told that...
I see that...
The Wikipedia entry on evidentials gives examples from Eastern Pomo, which has suffixes to mark different source of information: -ink’e (nonvisual sensory), -ine (inferential), -le (hearsay), -ya (direct knowledge). This is not the same as irrealis mood. Whether you think your neighbour's house is burning because you felt the heat of the fire (nonvisual sensory), because you saw smoke (inferential), because your other neighbour called and told you (hearsay), or because you set it on fire yourself (direct knowledge) doesn't influence whether you think it's true.