Yes, the English terminology is confusing and indeed we can't get encyclopedic. I think the glosses for 負極 and 正極 are about as good as we can get. People digging more deeply can see Hendrick's useful comments.

Unfortunately it is not as simple as I had thought: I have a background in electronics, and there the anode (both in a vacuum tube or a semiconductor diode) is positive and the cathode negative (see also https://en.wikipedia.org/wiki/Anode, sections "vacuum tube anode" and "diode anode). So I checked into this matter and found out that in an electrolytic cell (part of a battery), the anode can be either positive or negative depending on whether the cell is charging or discharging. So one could say (as a first approximation) that an anode is the positive terminal in a device to which an external voltage is applied to make same device work, while it is the negative termincal in a device that causes or produces a voltage. Anyway, we always run up against the limitations of a dictionary that cannot be an encyclopedia. :)

GG5: the anode; the negative 「pole [terminal]; a negative electrode.
Eijiro: チウム負極 : lithium anode
For 正極 we see:
GG5: 【電】 a cathode; 【物】 a positive electrode.
中辞典: 〈電池の〉 the cathode.

No, it's the anode.
It doesn't seem to be used for magnetic poles.

@@ -11,0 +12 @@
+<gloss>anode</gloss>
@@ -13,2 +14 @@
-<gloss>cathode</gloss>
-<gloss>south magnetic pole</gloss>
+<gloss>negative electrode</gloss>

https://ja.wikipedia.org/wiki/電極

Added an external reference

Correction needed: "cathode" and "anode" reversed with 正極 and 負極

@@ -13 +13 @@
-<gloss>anode</gloss>
+<gloss>cathode</gloss>