"Another [quality]" im Magic means the same as "a different instance of [quality]", or "any [quality] except itself".

As the one who brought up the question originally, I couldn't decide which English interpretation was correct - both would be fine under the rules of English. However, with the implications of that interpretation becoming quite non-sensical for Anafenza, the Foremost, it must be clear that "A' or another A" does not mean that A and A' have a mutual link between their meanings that changes as the stated quality for A' changes. A' is not a special case of the general A, because card text cannot be written with all possible card interactions in mind. "A' or another A" meaning they are related is true if and only if considered in a vacuum, i.e. without other cards that change the relevant qualities of one or both of A and A'.

The only sensible interpretation is that A and A', separated by "another", have no causal link, and it simply means that they have to be different players/objects, in addition to the stated qualities.

Therefore, if Ivy Lane Denizen has Nim Deathmantle equipped, Grizzly Bears entering the battlefield will trigger Denizen. Lantern Scout with Conspiracy (Bear) in play will trigger on itself, and Anafenza will trigger whenever it attacks and you have a different creature that is also tapped as a valid target.

"Another [quality]" im Magic means the same as "a different instance of [quality]", or "any [quality] except itself".

As the one who brought up the question originally, I couldn't decide which English interpretation was correct - both would be fine under the rules of English. However, with the implications of that interpretation becoming quite non-sensical for Anafenza, the Foremost, it must be clear that "A' or another A" does not mean that A and A' have a mutual link between their meanings that changes as the stated quality for A' changes. A' is not a special case of the general A, because card text cannot be written with all possible card interactions in mind. "A' or another A" meaning they are related is true if and only if considered in a vacuum, i.e. without other cards that change the relevant qualities of one or both of A and A'.

The only sensible interpretation is that A and A', separated by "another", have no causal link, and it simply means that they have to be different players/objects, in addition to the stated qualities.

Therefore, if Ivy Lane Denizen has Nim Deathmantle equipped, Grizzly Bears entering the battlefield will trigger Denizen. Lantern Scout with Conspiracy (Bear) in play will trigger on itself, and Anafenza will trigger whenever it attacks and if there is an object other than Anafenza that is also a tapped creature you control.