It is a good question. Let me see whether I can provide a summary. Sometimes it helps to write in point form.
1. Dhamma and Dharma: Dhamma is the Pali word and Dharma is the Sanskrit word for it.
– But it is best to avoid ANY Sanskrit words in Buddha Dhamma. There is a reason why the Buddha prohibited bhikkhus from translating the Tipitaka to Sanskrit. We see the disastrous consequences of translating “anicca” to Sanskrit as “anitya.” While ‘anitya” in Sanskrit means “impermanence”, “anicca” in Pali has a much deeper meaning.
2. The PRIMARY meaning of dhamma is “to bear.” Everything in this world has arisen due to causes. Those causes are dhamma (usually it is written in the plural, dhammā)
– In that sense, dhammā are “kammic energies” that are in kamma bhava. As we know such energies (kamma bhava) arise via Paticca Samuppada.
3. There are “good dhammā” that can bring “good vipaka”.
– Then there are “bad dhammā” that bring “bad vipaka”, and thus they are called “adhammā”
– Thus adhammā are just the bad version of dhammā
– Note that adhammā arise due to lobha, dosa, and moha, while dhammā arise due to alobha, adosa, and amoha.
4. Buddha’s unique teaching was “sabbe dhammā anattā“.
– That means ALL dhammā, including adhammā are of “unfruitful nature”.
– As we know, adhammā lead to rebirths in the bad realms and dhammā lead to rebirths in the good realms. That means all types of dhammā bind one to the rebirth process.
– That is why “sabbe dhammā anattā“, i.e., “all dhammā are unfruitful”. That includes “good dhammā” due to alobha, adosa, amoha.
5. Now, Buddha Dhamma (where the dhamma is without the long “a”) is teaching or a procedure.
– Buddha Dhamma explains how one can stop creating both types of dhammā that keeps one bound to the rebirth process.
– There the Buddha comes from “bhava” + “uddha” where “uddha” means to ‘root out”. Thus “Buddha Dhamma” teaches one how to stop those bhava/kammic energies/dhammā from arising.
6. It is best to disregard other definitions (at least until evaluating the soundness of the above explanation).
– For example, Dipobhasaddhamma quoted: “Having lent ear, one hears the Dhamma. Having heard the Dhamma, one remembers it. Remembering, one penetrates the meaning of the teachings. Penetrating the meaning, one comes to an agreement through pondering the teachings.” from MN 70. “Dhamma” there refers to Buddha Dhamma, so it is consistent.
– If any contradictions with the Tipitaka can be presented, I would be happy to discuss them.
7. I purposefully made the explanation short to emphasize the main points. Please feel free to ask questions.
P.S. To understand #4 above, one needs to understand that puñña kamma (moral deeds) done with alōbha, adōsa, and amōha give rise to births in the human and higher (good) realms. Thus puñña kamma are necessary to get good rebirths, but not good enough to attain Nibbana. If one remains in the rebirth process, one WILL be reborn in an apaya sooner or later.
– Such puñña kamma automatically become kusala kamma upon comprehending the Four Noble Truths/Paticca Samuppada/Tilakkhana.
– Puñña kamma keep one in the rebirth process (via akusala-mula Paticca Samuppada), while kusala kamma lead to Nibbana (via kusala-mula Paticca Samuppada).
– That is a subtle point some people miss.
– See, “Kusala and Akusala Kamma, Puñña and Pāpa Kamma“