Four Avos Nezikin

The first mishna in Baba Kama discusses the 4 avos of nezikin - shor, bor, maaveh, and hever. Then, at the end of the mishna the mishna presents the "tzad hashaveh" between the 4 avos. They are all accustomed to doing damage, and you have to watch them (darkan lehazik and shmirasan ulecha). The question is that if there is already a tzad hashaveh so why do we need 4 separate avos? Why doesn't the mishna just say that one is chayav for anything which is darkan lehazik and shmirasan ulecha? What difference does it make if it is shor, bor, maaveh, or hever?
The gemara in Baba Kama on daf 5a answers this question by pointing out that we need the avos "for their [individual] halachos" (lehilchoseihen). So bor is needed because bor is patur on keilim, and shen and regel are patur in reshus harabim etc.
We can now probe further and ask the following question. Are the 4 avos needed as separate mechayvim or are they needed as separate potrim? Let us take bor as an example. Does bor have a separate mechayav of "a chalos shem bor" that is patur on keilim? Or is the mechayav of bor the same general mechayav of all nizkei mamon? This would mean that the tzad hashaveh of darkan lehazik and shmirason ulecha is the mechayav of bor and that once something has a "shem bor" it gets a ptur on keilim. The shem bor would then only relate to the individual halachos and not to the general mechayav.
What is the nafkah minah, the practical difference, in all of this? A simple nafka minah would be a "hybrid" nezek. What if we had, for example, a type of damage that was neither shor or bor but learnt out from the both of them with a tzad hashaveh? If the "mechayavim" of shor and bor are different, so we can only learn out that which is most kal, and this hybrid would be patur on keilim. If, however, the general mechayav is all the same, so only bona fide bor gets the ptur of keilim, and our "hybrid" case would not be patur on keilim. See the Gri"z on the Rambam in Hilchos Nizkei Mamonos where he discusses this issue in more detail.
Finally, in terms of shitas Rashi it is interesting to consider the two leshonos in rashi on daf 3a in Baba Kama whether to learn out bor of 9 tefachim from a diyuk in the pasuk or from the pasuk explicitly. This may be relevant to our issue of whether an av is a separate mechayav or a poter. Also relavant may be the issue on 3a/3b of placing a stone, satchel, or burden in reshus harabim and what dinim this has. This may in fact be a case of a "hybrid" nezek, see Rashi and Tosafos there.