Vayikra chapter 11 records different animals that can be eaten (that is to say they are kosher) and animals that cannot be eaten. After the introductory sentence, Vayikra 11:2 records, “These are the hayyot that you can eat from all the behamah that are (is) on the land. Which animals are classified as hayyot and which animals are classified as behemot?
In modern Hebrew the definition of hayyot are wild animals and behamot are large domesticated animals. I believe that this definition derives from the halakhah of kosher animals. Devarim 14:4,5 record, "These are the behamot that can be eaten: ox (cows), sheep and goats, gazelle, deer, roebuck, bison, antelope, wild goat, ibex, and mountain sheep." The Rambam (Laws of forbidden foods, 1:8) writes that the animals listed in Devarim14:4, the ox, sheep and goats are behamot, while the other seven animals listed in Devarim 14:5 are hayyot. The Rambam (Laws of forbidden foods, 6:1, also see Rashi on Devarim 14:4) also writes that hayyot are a sub-category of behamot. This definition has important practical implication. Vayikra 17:13 records that if a person hunts (kills) a chaya (or a bird), then the blood of the animal has to be covered with dirt. Based on this verse, the blood of an animal that is classified as a behama does not have to covered with dirt.
I do not understand this distinction between hayyot and behamot since Devarim 14:4 records "These are the behamot that you can eat" before the list of all ten animals, and there is no mention of hayyot in the verses. It seems obvious that the ten animals listed in Devarim 14:4,5 are behamot. In addition, hayyot, based on the name, living things (see also Vayikra 11:47), refers to all animals, and then behamot are a subcategory of hayyot. With regard to Vayikra 17:13, according to my more expansive definition of the term behamot, the blood of all the animals listed in Devarim 14:4,5 do not have be covered, which would be a leniency. Note with regard to which animals can be eaten, the difference between my understanding and the traditional understanding is just a question of semantics since there are still just ten land animals that can be eaten. It is just that I think that all ten animals listed in Devarim 14:4,5 are behamot, while the traditional view lists three as behamot and seven as hayyot. However, the different definitions of the term behamot lead to some differences how to understand various verses in the Torah.
If we return to 11:2, the verse means these are the hayyot, the animals, that can be eaten: (Example one:) With regard to the behamah, a sub-category of hayyot, (animals that move) on the land. And then 11:3 explains that “with regard to the behamah” means those behamot that have split hooves and bring up their cud can be eaten. Thus, some behamot can be eaten, while others cannot be eaten. Afterwards, 11:9 records a different sub-category of hayyot, example two, animals that move in the water that can be eaten, and 11:13 records a third sub-category of hayyot, example three, animals that fly that cannot be eaten.
Another example is Vayikra 7:25, which records “for whoever eats helev (fat) from the behamah that is offered as a sacrifice…” This verse means that there are some behamot which can be offered as a sacrifice and some that cannot be. If the term behamot refers to the ten animals (or more) listed in Devarim 14:4,5, then there exists the possibility that some behamot are offered as sacrifices and some are not. However, if behamot are only ox, sheep and goats, then all behamot can be offered as sacrifices, and Vayikra 7:25 cannot be understood in its simple sense.
In addition, Vayikra 11:26 records that any behama that has hoofs but the hoofs are not split and does not chew its cud is tamei. Yet, if behamot are only ox, sheep and goats, then all behamot have split hoofs. Instead, 11:26 is noting that some behamot do not have split hoofs, such as horses, donkeys, zebras (see Luzzatto on 11:26) and these behamot differ from animals whose hoofs are split and chew the cud who are kosher and not tamei. This distinction between behamot that are tamei and those that are tahor is also recorded in 20:25.
11:27 then records that any animal that walks on its paws among the hayyot that walk on four legs is tamei. This implies that an animal that walks on paws (bears, cats, dogs?) is a type of hayya, but it is not a behama. This means that a behama is a hoofed animal (ungulates) and all the animals listed in Devarim 14:4,5 seem to be ungulates. (Note that Rashi on Shemot 14:7 seems to define horses as being behamot, which supports the idea that animals that have hoofs are behamot.)
Some other verses where the two terms, hayyot and behamot appear are in Bereshit 2:19,20, by the Garden of Eden. In Bereshit 2:19 the Torah uses the word hayya when referring to all land animals. In the following verse, 2:20, the Torah separates out the behamot (deer? sheep?), the sub-category of hayyot, from all the other hayyot in the Garden of Eden. 2:20 also refers to the behamot before the remaining land animals, hayyot, maybe because Adam was more likely to have found help (ezer) from these animals, the ungulates, who are relatively tamer than the hayyot.
Another case is in Bemidbar 35:3, where first the behamot are listed since they are more likely to be in one's field since some of them are raised for food or work, and then the general term for all animals, who may happen to be in one's fields (i.e., dogs? birds?), hayyot is recorded.
There is a third term in the Torah for a group of animals, mikneh, livestock, cattle, sheep, pigs and horses(?). Behamot are a larger category of animals than mikneh, as all mikneh are behamot but not all behamot are mikneh. Thus, Bereshit 36:6 starts with the smallest group, the mikneh, then it becomes more expansive, the behamot, all ungulates, which would be horses and donkeys, and then it refers to all possessions. In Bemidbar 31:9, the Torah first refers to women and children, then to behamot, the larger group of animals, and then to mikneh, the smaller group of animals.
In Tanakh, Micah 5:7 records that lions will eat behamot in the forest, but farm animals like cows, sheep and goats usually are not living in the forest. On the other hand, deer, antelopes and gazelle do live in forests and are eaten by lions.
After writing this, my son Yishai, pointed out to me that this discussion of what animal is defined as a behama is not new. Ibn Ezra in his commentary on Tehillim 8:8 quotes from the Karaite commentator Yefet that behamot refer to animals who eat grass, which would be ungulates, but Ibn Ezra rejected this interpretation since Mishlei 30:30 refers to a lion as being a behamah. Note Ibn Ezra in his comments on Bemidbar 31:30 refers to camels as behamot, and if a lion is considered a behama, then this would also contradict the traditional definition of the word behama. I am not convinced by this refutation from Mishlei since a verse from a prophetic writing is not sufficient to overturn the simple understanding of the verses in the Torah. It could be that the definition of the word behama changed from the time of the Torah to when Mishlei was written. Also, maybe, one can understand Mishlei 30:30 that it means that lions, who are not behamot, are stronger than behamot, which includes rhinoceros and hippopotamuses.