ATK vs. ATK Rolls vs. ATK Dice Rolls vs. Damage

I'm sure the answer is simple for this but a few questions came up while playing.

Assuming Damage Rolls and Attack rolls are the same, can someone help me clarify what to do with a couple of cards, for example "The Hero" and "Flame of the Infinite".

"The Hero" says to add +1 to HIT and ATK rolls, that just means a +1 modifier correct? Not extra dice.

"Flame of this Infinite" says +5 ATK and +1 ATK Dice Roll/HIT Roll. Does that mean roll an extra die when attacking/hitting or just adding another +1 Modifier (Making it +6 ATK)?

Where I got confused was "Dark Elf" where you can add 4 extra damage dice... could be the gummies talking.

Thanks for the help, Ward-Gourds!