There are many words in the suttas to describe the broad variety of mental experiences that you are interested in.
Usually, hatred and ill will are synonymous in English and that seems well founded from the Pali, but I wouldnt say the same for ill-will and anger either in English or in the Pali. However, both can be contained under the root defilement of Dosa, and also with the underlying tendancy (anusaya) of Patigha of aversion or resistance.
In terms of the lower fetters it’s worth noting that mostly in the suttas the 5th lower fetter is Byāpāda but in the Abhidhamma (Dhs. 1113-34) we have Patigha instead, which is often translated as anger in that context. Unfortunately, many writers often incorrectly substitute Patigha for Byāpāda and so we have the ongoing confusion of ‘anger’ being a lower fetter when that is not the case in the suttas.
Something I often emphasise in teachings about ill will, hate anger etc is to avoid the unrealistic expectation that we can just expect these things to be uprooted easily - beware the tendencies of spiritual bypassing (emotional numbing, anger phobia, toxic positivity, deluded belief of attainments) which folks in spiritual communities often idealistically gravitate toward, creating unrealistic expectations of themselves and others.
Afterall, the fetter of ill-will is not completely overcome till the 3rd stage of enlightenment - non-returner (or anagami) stage. This is an incredibly high stage of development, just one step away from full liberation (or arahantship). So, it’s unrealistic to expect that us ordinary, everyday people wont still have a bit of ill will or anger from time to time.
The analogy I often use to help people put this in perspective is that of a trip to the moon. We are stuck on earth and getting to the moon is hard. If arahantship is stepping on the moon, then anagami, when ill will is eradicated completely, is touchdown in the lunar lander. Before that was getting into lunar orbit (once returner, where ill-will is substantially reduced) and before that we needed a HUGE amount of energy and fuel to escape earth orbit - stream entry. This took a massive amount of effort and understanding of complex ideas, but yet there is still ill will in the mind! And, most of us are still back here looking up at the sky, with no inkling of how to get into space at all. A few of us might be drawing cartoons of rockets, or if we are lucky, reading instructions (the Buddha’s teachings) on how to build a rocket at university or perhaps working for NASA. But the sad truth is that certainly most of us will never get into space in this lifetime… so if people get a little angry or hostile from time to time, we can understand why - like us, they are a long long long way from the moon…
To me, anger is less of a problem that resentment, grudge, malice, malevolence etc because these things are thoughts that we let percolate inside us, returning to over and over, deepening and cementing that hate. But anger is usually something more specific, spontaneous and, therefore, hopefully more short lived.
A good example of this is the Lekha Sutta An3.132 where three types of angry person (in this case the Pali is khujjati) are compared to inscriptions - the first is an inscription carved into rock (holds on to anger for a long time), the second is an inscription in sand (holds on for a lesser time) but the best is the third, a line drawn in the water - which disappears almost as soon as it is drawn, which is how we should practice. We don’t have the unreasonable expectation that anger wont arise in us (it will) but when it does, it’s *how * we deal with it that matters most- letting it go quickly.
See below for some terms in the Buddhist thoughtscape of aversion/hate/ill-will.
Dosa: Aversion, Hatred,
- one of the Three Unwholesome Roots or ‘poisons’ (akusala-mūla)
Byāpāda / Vyāpāda: Ill-will, malice, malevolence
one the Five Hindrances (nivarana)
one of the Ten Fetters (samyojana),
one of the Defilements (kilesa)
one of the 3 Wrong Intentions (asankappa)
one of the 16 Defilements (upakkilesa)
Patigha: repugnance, grudge, resentment, anger
one of the Nine Latent Tendencies (anusayas) and one of the Abhidhamma’s list of the 10 fetters, coming in at number 2 on the list. Byāpāda is absent in this version.
Kodha: anger (one of the upakilesas)
kujjhati gets/becomes angry with, cross with something
Vera: enmity, hatred
Vihiṃsā: cruelty, harm, hurting, one of the 3 unwholesome intentions
Upanāha: hostility, hatred
Āghāta: resentment, ill will