Hello,

The simple answer is entirely up to you as the player. When I designed the scenarios you've described it was from the following stances:

The Original Game didn't have tokens for the Rivals - You always battled the card. That's fundamentally why all Rivals have their own unique attack values directly on the card. These values are based on Kanto to keep things balanced. So that you can play the original rules in any region.

Tokens were then added to facilitate 3v3 battles & Gym Leader Expansion, at that stage all the player-use tokens already existed, so Rival tokens were just copied from their token counterparts and Gyms became as hard as the token-balance dictated.

The above reasons are why you will see instances such as Brock where his card is nowhere near the same power as his token - Because Onix the token is stronger by nature of being a red token than Onix the rival.
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To directly answer your questions:
> I see there are rival cards included with the pokemon that each gym leader uses and I'm a little confused about how I should go about that.
That's to facilitate game configurations that don't use the gym leader expansion.


> the rival cards are of course the leader's signature pokemon, but there's also a token for their signature pokemon included as well. Are the rival cards separate from the tokens or do they redifine the pokemon in the battle.
Answered above as to why this exists, If you're playing with 1v1 battles, decide at the start if you are battling the card or whatever token is pulled from their inventory. If you're playing 3v3 then you battle the tokens accordingly.

Remember that as in the rules, if you choose to battle the tokens rather than the rival cards, the tokens do gain the +attack bonus on the card based on their roll.