Okay, so I've always viewed metalcore as hardcore bands from the late-80s through the 90s with metal influence, like Inside Out, Integrity, Snapcase, Mean Season, Unbroken, Unashamed, Strongarm, Despair, Slugfest, Buried Alive, and others of that sort. This style, in my opinon sort of continues today with bands like Burial Year and much of the Deathwish roster like Cursed (RIP; there's a big sludge and crust element there), Pulling Teeth (also RIP; basically sound like intense death-influenced thrash metal with some hardcore vocals), and Nails (plenty of grindcore in that sound).

Mathcore was the more discordant, technical style associated with metalcore that arose in the mid-90s, like Starkweather, Coalesce, Deadguy, Cave-In, Botch, Dillinger Escape Plan, and Converge-- still very much a part of the hardcore scene.

Melodic metalcore was like metalcore, but with the hardcore part replaced with post-hardcore: Eighteen Visions, Vision of Disorder, Atreyu, Norma Jean, Bleeding Through, Scarlet, Training for Utopia, etc. This sort of continues today with bands like the Ghost Inside.

I think there are a lot of people who would probably agree with me up to this point, but here is probably where opinions will diverge.

Deathcore is hardcore with death metal influence, obviously. So I would say that this is stuff like Earth Crisis, All Out War, Merauder, Overcast, and Bloodlet. Hatebreed, down in Connecticut, saw the NYHC and NYDM scenes mixing, added a dollop of Obituary, and made tough guy beatdown moshcore or whatever you want to call it-- the kind of thing that bands like Terror later trafficked in. When it comes to what most people consider deathcore now, I would probably only extend this to maybe early Despised Icon or the Red Chord, but as for my "hardcore-with-death-metal-influence" definition, I think only bands like Bury Your Dead, early Liferuiner, the Acacia Strain and Xibalba (not the black metal band, of course) would qualify; maybe Animosity and Dead to Fall.

Now, up where I was defining melodic metalcore, some people might have added Darkest Hour, Shadows Fall, Unearth, etc. but I never heard any hardcore influence in those bands whatsoever. They're basically American melodeath to me-- can anyone point out the hardcore influence? Maybe there's a little in the vocals of Darkest Hour and Shadows Fall.

Now, about modern deathcore, like Suicide Silence, Whitechapel, Emmure, Winds of Plague, and that ilk, I fail to see the hardcore influence. Remember, the modern breakdown came from Suffocation and Dying Fetus, and later Internal Bleeding and Pyrexia. Those early bands basically just sound like either generic death metal, death mixed with some nu-metal, or symphonic death metal.

A lot of the modern bands being labeled metalcore (A Day to Remember, Asking Alexandria, Enter Shikari) are pretty much just post-hardcore or easycore, while the modern label of deathcore is nearly meaningless.

Any thoughts on this? Does anyone have recommendations based on my definitions?
Modern metalcore and deathcore DOESN'T have Hardcore influence for the most part.

There are Metalcore bands, some of which you already mentioned that are based on Hardcore but are what most refer to as Metallic Hardcore these days, there's a thread about those bands here: https://www.ultimate-guitar.com/forum/showthread.php?t=1598330

As for Deathcore? The only one that comes close to Animosity. There's no Death Metal in The Acacia Strain that can give it the title Deathcore. It's just heavy ignorant hardcore.
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Despised Icon had a lot of hardcore influence in their earlier stuff.
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