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Attack Throw = The Roll-chance to land a Hit.
Attack rolls are your chance to hit things. You'd roll a d20, and add your bonuses to attack and then compare that too-
Armor class (AC for short) is your defense essentially. It's how hard you are to hit. If someones attack roll meets or exceeds the targets AC the attack will hit, otherwise it will miss.
1.) An Attack (or Spell attack)
For this you roll a D20, add your modifiers from Strength, intel, proficiency, etc. total it up.
Then you compare that to the Target’s AC (Armor class).
If my AC is 18, your total attack needs to be 18+ to hit me, or else you miss.
2.) Spell save D/C.
Your attack will say XXX save (Example: WIS save, or DEX save).
You have a set save, that is 8 + Spell save mod (you casting stat) + Proficiency bonus + other mods.
If you have 18 charisma as a Sorcerer and a +2 proficiency, you cast fireball…it’s a DEX save of 8 + 4 (Cha) +2 (prof) = 14.
This means the target rolls a d20, adds Dex modifier, and must beat a 14 to make the save or suffer the consequences of the spell