Yes, but it has not always been consistent, so it will sometimes depend on the card in reference. If a card refers to a “Character” then it is referring to all instances of dice of that character. If you are counting active characters, then you would count how many unique character dice are in the field (e.g. Half-Elf Bard).

If it refers to a “Character Die” then it would refer to a single die of that character. If you are counting Character dice, then you would count all active dice.

If it says “target character” then you will be targeting a specific character die.

Finally, if it states “Name a character”, it is referring to a character card (so all corresponding character dice would be impacted). Note: you cannot name “Sidekick” since it does not have a card.

From the rulebook:

“Some cards will have you check how many of a certain type of character are active. If an effect gave +1A for each active character, and you had 5 Character Dice in the Field Zone (3 different characters) and your opponent has 1 character die in the Field Zone, the effect would grant +4A (even if your opponent’s character was the same name as one of yours). If it doesn’t specify your characters, it checks yours and your opponent’s active characters or dice.”