So far, the currently available Counter doesn't possess any other parameter other than name and icon. Ability and effect that interacts with Counter also refer to the Counter simply by their possessed icon.
Acquiring and Expending Counter
Certain ability or effect may instruct the player to "acquire" (得る) or gain an amount of Counter. To do so, the player add an equal amount of Counter Marker under their possession during the course of game.
Conversely, certain ability or effect may instruct the player to "expend" (消費する) or remove an amount of Counter instead, in which the player have to remove an equal amount of Counter Marker under their possession during the course of game.
Similar to Token, it is mandatory to bring the dedicated Counter Marker (カウンターマーカー Kauntā Mākā) when using cards that allow the player to acquire or expend a Counter.