In allomancy, the metal is just a catalyst. It helps an allomancer open a channel through the part of preservation that resides in them and draw on Preservation's power. I think I read that in an annotation.
I recall from the chapter headings that allomancy comes from Preservation, hemalurgy comes from Ruin, and Feruchemy is of the balance. That's not explained any more than that, but I can speculate. Allomancy uses metal as a catalyst to draw on Preservation. Hemalurgy stores an aspect of a victim's body in a piece of metal and transfers it to another. Feruchemy allows one to store aspects of one's own body in metal, to be drawn out later.
Nightblood is similar in this respect to both hemalurgy and feruchemy. A bit of one person's soul (the Breath) was transfered willingly from one person to another; that person amassed quite a lot of Breath and stored 1000 of them in Nightblood. This mass of life force has managed to imbue the inanimate metal with the characteristics of human sentience, which itself probably (my guess) has something to do with the shards of Adonalsium, which, again, has something to do with the fact that metal inside a person can't be pushed or pulled.
(Honestly, I think metal inside a person can't be pushed or pulled because, were that not the case, Allomancers and Hemalurgists would have an excessively debilitating weakness. Clearly that requirement led to lots of in-world rationalizations.)
But I'm just rambling to take a break from studying. Sorry you had to read that bag of wind.