The words detached and detachment are not the same.

Detached: showing no emotional involvement

Detachment: (philosophy) the state of lacking material desire

Neither word in my opinion captures a comfortable state of being, either empirically (demonstrably)  or logically (intellectually). It isn’t merely a balance of participation and neutrality or emotional and physical. In fact in both instances it is more a matter of caring or not caring, whether viscerally or logically removed.

I normally show “emotional involvement”; and, I am shamefully far removed from immaterialism or whatever the proper term for “lacking material desire” may be. I doubt the distinction between detached and detachment is meant to imply that if one were to show an interest in stuff, that amounts to emotional involvement. Nonetheless  I am hopelessly materialistic (metaphorically and emblematically consumed by worldly matters). I like things and matters of this world. In fact I tend to get emotionally involved with things (in an artistic way naturally). I think that based upon any analysis I am beyond the definition of “lacking material desire” if only because I tend to pursue the substantive in everything; and I seldom if ever resort to the metaphysical for improvement or iteration. It Is in my nature to become both emotionally involved and psychically attached to the most mundane features whether a large tree stump, the mounting corn stalks, the ivy curled about a gnarled and grey country fence, the direction and speed of the wind as apparent in the shifting face of the leaves of the trees, the colour of the flowing river water.

George Berkeley is credited with the development of subjective idealism.

Subjective idealism, or empirical idealism or immaterialism, is a form of philosophical monism that holds that only minds and mental contents exist. It entails and is generally identified or associated with immaterialism, the doctrine that material things do not exist. Subjective idealism rejects dualism, neutral monism, and materialism; it is the contrary of eliminative materialism, the doctrine that all or some classes of mental phenomena (such as emotions, beliefs, or desires) do not exist, but are sheer illusions.

This hardly gets one any closer to a fundamental understanding the base word detach. But it certainly invites a tone of delinking or breaking off of relations. And while both are possible, neither is part of my vernacular. As erratic as I may be, I am never emotionally uninvolved nor other worldly. On that broad spectrum, I am both emotionally involved and substantively inclined. To interpret that status as fortuitous or otherwise is entirely another matter. Detached and detachment are simply variable states of palpable association.  Neither is descriptive of the nature of the association. That is a subject for deeper investigation (though admittedly it is generally an indication of the degree of both meaningful involvement and gravitated interest). As usual the discussion of words descends to the unwritten commonality of life. It all connects.