Kingsvein hugely changed the combat engine of the game. While at its most basic level, it's the same as what you know and love from Horizon's Gate, what was built off that is highly different.

Let's start with the most important change.
The initiative tracker at the top of the screen looks the same as before, but the time amounts have been removed. Each side of the fight takes its turn one after the other: first all your characters act, then all surviving enemies, and back and forth. This means you no longer get benefits from skipping your turn if you don't have a good move (other than not putting yourself in a bad position). You can select one of your other characters by clicking on them, so your characters can act in whatever order you like. Delayed effects always trigger at the start of your next turn, so both you and enemies will always have a chance to escape them. If you want to land a hit with a delayed attack, trap the target in one place or reduce their movement enough that they can't escape.

In Horizon's Gate, you would occasionally have the opportunity to alter terrain to your advantage: for example the spell Condensate creates a puddle of water which can be electrified.
Kingsvein takes this to an entire new level. In addition to the classic damaging spikes and exploding barrels, Kingsvein boasts several interesting new terrain features. The game will usually warn you of their locations when you use a relevant ability, as shown above. Some terrain can be hard to see, especially blood and oil, so don't be afraid to open up a lightning or fire spell just to check where the puddles are, then close it to make your move.

• Blood: The most common terrain feature besides Rubble. Blood spawns whenever a creature takes physical damage. Like water in previous games, blood increases electrical damage and conducts a small amount of electrical damage to adjacent blood tiles. In large fights, blood can significantly build up and become both a significant aid to your electrical mages and a significant risk to your own characters.
  
• Fire: Fire is created whenever a fire spell hits an empty space. Much like spikes it can be jumped over and deals a small amount of damage when stepped on, then is extinguished. Fire will melt ice and ice will extinguish fire.
  
• Ice: Ice is created by ice spells, naturally. Ice hampers jumping, reducing jump distance by 1 (which will prevent most characters from jumping at all). It also doesn't count as a tile for push distances. Characters just slide across the ice when pushed. This can be particularly deadly near pits and ooze.
  
• Pits and Ooze: These are basically the same thing. Ooze is like water in Horizon's Gate. A character knocked in is out of the fight unless somehow pulled out (I expect a Chisel's Chain ability to work but haven't actually tried it). Pits are worse. A character knocked in is completely unrecoverable until the fight ends, so be on your guard. They mostly appear in the lategame. Both of these are great to use against your enemies as well, with skills like Chain, Thunderbolt, and Bombardment being excellent forced-movement tools.
  
• Oil: It's rare, but useful. Oil can be created using the Catalyze spell. When exposed to fire, oil ignites, dealing fire damage to all creatures in the oil (much like blood spreads lightning damage, but nastier) and igniting new fires on all empty tiles within the oil.
  
• Spikes: You know this one from past games, and they're the same as always. If you step on them, you take physical damage and they turn into Rubble. The big difference is now you'll have the ability to create them, with skills like Caltrops and Gate: Stalactites
  
• Rubble: You know this one too. Rubble costs 2 points of movement. That's it.

You probably noticed as soon as the first fight that your characters only have 10-15 health and deal 3-5 damage. All numbers have been reduced in Kingsvein... Except bosses' health, they still get hundreds. They often take clever tactics to defeat.

Following from that, equipment is less powerful than it was, although it's still as powerful relative to other items. More importantly several things have changed.
There are only 3 melee weapon types. Axes, daggers, and whips have been removed and hammers have been mostly removed (a few still exist but the hammer skill doesn't).
The remaining melee weapons are swords, spears, and flails. Swords deal +1 damage, spears hit the tile behind the target, and flails can attack diagonally, just like before.
Ranged weapons are unchanged. Crossbows deal +2 damage relative to bows, but must be reloaded after each shot.
Armor no longer reduces damage taken, instead it provides an HP bonus and maybe an MP bonus depending on the type.
There are only 3 equipment tiers: rusty, ore, and corpryst. Rusty is equivalent to wood, ore is equivalent to iron and corpryst is equivalent to steel. There are legendary items scattered around, which are usually as good as corpryst and have additional special effects.

The classes have changed. I'll leave the in-depth overview for someone else's guide (I haven't extensively played every class yet), but here's a short summary.

• Knight: Shares many abilities with Warrior but the effects have changed so pay attention. This will be your character's starting class.
  
• Mystic: The other base class, similar to Scholar in role (as a versatile caster) but with completely different spells.
  
• Chisel: A melee debuffer similar to Rogue.
  
• Vanguard: similar to Defender, with pushing, healing, and protective buffing abilities.
  
• Fanger: The first (but not last) class with completely new abilities, Fanger is focused on field control by creating traps and spikes, and inflicting Bleed. It has good pushing and pulling too.
  
• Marksman: The only class to specialize in ranged weapons (other classes' special attacks require melee weapons). Doesn't map cleanly to any Horizon's Gate class due to having a lot of new abilities, but most closely resembles Sharpshooter.
  
• Melder: Your dedicated healer, similar to Sage. Melders have less direct healing, but can spawn healing Growths to passively assist. They also get earth-based area control spells for extra fun.
  
• Ashen: A fire and lightning based spellcaster. These guys are powerful blasters with some interesting abilities revolving around fire and blood terrain.
  
• Marshal: Very similar to Tactician. You can prompt allies to attack or move, or give them minor healing and cure status effects. Judging by the icon and passives, they are intended to use a spear.
  
• Titan: A brawler with a mix of pushing attacks and earth spells.
  
• Dragoon: A dual wielding warrior who also gets a couple tools to aid in magic if they have a magic class for their secondary. I have no idea why they require Marksman XP.
  
• Mancer: A mage specializing in delayed spellcasting. Some abilities inflict conditions that trigger after a certain number of turns.
  
• Eidolith: A light-themed mage who Blinds enemies, can dispel magic, and can even turn allies invisible or spawn a clone of themselves.
  
• Crysolith: An ice mage. In previous games, Graven creatures were weak to ice. That's not a thing here (instead non-Graven creatures are resistant to ice). However the Crysolith has a good set of area attacks based around creating and manipulating ice, with some ability to freeze enemies, conduct damage through ice, and push enemies around.
  
• Gatekeeper: The only returning class remains focused on large area attacks with an added ability to teleport itself. However it has a new set of specific abilities it uses for that purpose.

A few additional notes on classes:
The tree looks like it has 3 base classes, but the middle class, Chisel, is derived from Knight.
All of the classes in the Knight tree are melee-only except for Marksman. Fanger has the Ranged Weapons skill but none of its abilities are weapon attacks so it can be either.

Skills have been streamlined. There are only 4 weapon skills: Sword, Flail, Spear, and Ranged. Similarly, magic skills have been paired off: fire and lightning are under Blaze, ice and ruin are under Ruin, and physical spells are under Geo. There are a few extra skills such as Channeler, Defy Death, and Teamwork, which have other more obscure effects, and of course the basic stat increasing skills as well.

Thanks for reading, I hope this guide is helpful.
Good luck out there, Wisp Slayers!