Two English terms cover most of what is written on this subject, and both came from somewhere specific before being applied everywhere.
Totem entered English from Ojibwe, where the underlying word concerns clan membership and descent. Nineteenth-century anthropology took it up as the name for a supposed universal stage of religion, and totemism became a category applied across four continents. It was dismantled in the twentieth century by writers who showed that the practices grouped under it had little in common beyond the observer's expectation, and the word survives mainly as a caution.
Spirit animal is more recent and has no single origin in any tradition. It circulates now as a general term for a personal animal guide, and it is applied backwards onto Native American traditions that use their own vocabulary for quite different relationships: a clan affiliation, a being encountered in a vision quest, and a helping spirit acquired through training are three separate things, and none of them is what the popular phrase means. Members of those nations have objected to the usage, both to the flattening and to its use in casual online speech.
The underlying subject is real and very widely distributed. Traditions across the world hold that particular animals are related to particular people, lineages or specialists, and that the relationship carries obligations.
The atlas names the tradition and its own term wherever it can, and uses the general labels only where a genuine comparison is being made.