Hexenbiests seem to be a very unique Wesen. Hexenbiests seem to be a symbiotic relationship between a human and a hexenbiest spirit.
In "Love Sick" Nick fights with Adalind and gets her to bite his lip causing him to bleed and some of the blood gets into her mouth. A few seconds later, the Hexenbiest spirit inside of Adalind leaves her body causing her to become a normal person, and lose all of her powers.
It is possible for a normal human to become a Hexenbiest. During the Contaminatio Ritualis, Stefania Vaduva Popescu says the ritual isn't a guarantee because Adalind has to be accepted by a new Hexenbeast spirit. After she is accepted, a hexenbeast spirit is seen entering into Adalind. ( Juliette Silverton is another example of a human becoming a Hexenbiest).
A Hexenbeast can only woge while possessed by a hexenbeast spirit, so the spirit is the source of the woge as well as the supernatural powers. Therefore, I don't think Hexenbeast is geneticaly linked at all, but instead comes from a possession of a Hexenbeast spirit. A Hexenbeast's daughter is most likely chosen and possessed by a hexenbeast spirit in utero.
After the above Hexenbiest analysis, Mishipeshu doesn't seem that different from a Hexenbiest. When Mishipeshu possessed someone, it appeared that they could partial woge (just eyes) like many other Wesen, as well as a more complete woge. Both Hexenbiest spirit and Mishipeshu give the host super-human strength. Similar to a Hexenbeast's spirit, Mishipeshu can be driven out of a person (for all we know, that red powder that Hector Ballou blew into Hank's face could have been powdered Grimm blood).
However, there are some significant differences. Mishipeshu completely controlled the human it possessed, whereas the Hexenbiest seems to control the Hexenbiest spirit. Also once paired with a human, a Hexenbiest spirit does not leave the Hexenbiest until forcibly removed (doesn't mean they cannot though, maybe the spirit is just loyal/committed to its host). Mishipeshu possessed and left humans at its own will.
Nevertheless, there are striking similarities between these two spirits.