Similar, but not quite. Animism is a belief that everything has a soul or spirit. Panpsychism can be seen in a religious sense spirit=mind but it is not necessarily so.
As an animist, I'll respectfully disagree with you on your definition of animism. Yes, that is the dictionary definition, based in Tylor's description back in the 1800s and pretty much accepted by anthropologists, sociologists, etc., ever since...until the last couple of decades, when there's been a renewed interest among scholars as well as indigenous peoples, among whom "animistic" beliefs and practices are most commonly seen. See, for example, Graham Harvey, Nurit Bird-David, etc. Harvey's recent Handbook of Contemporary Animism is a collection of writings by a wide variety of scholars and practicing animists.
Yes, in some senses, animism is about things other than humans having spirit or soul, but that is an attempt to push indigenous beliefs and practices that are quite unlike the Western tradition into Western conceptual categories. In practice it means that animists treat others in their environment as "other than human persons," whether we classify those others as animate or inanimate. Those other than human persons often share some traits with humans, among them volition and consciousness--and sometimes the relationship is closer, of belonging to a common ancestry or kinship group. Animism is about approaching those other than human persons in an appropriate social manner, following agreed-upon patterns of interaction, so that a proper balance between the various groups of persons can be established and maintained.
That's why I said that it sounds very animistic, and your further explanation here that "spirit=mind" fits very well with the idea that other "things" in the world may be "other than human persons." But I'll have to read up further to be sure. I don't remember coming across the term panpsychism in any of my readings in animism recently.
