Some games, like Daggerheart, keep money abstract so it stays out of the story's way. West Marches campaigns tend to track it, because what a character earns carries over from one adventure to the next and shows how far they have come.
In a West Marches game, characters can usually keep their money in town and don't carry all of it on an adventure. That makes it unnecessary to track coins that convert into each other, like copper, silver and gold, as separate currencies. In a D&D game, a torch can simply cost 0.01 gold, and nobody has to keep count of copper pieces.
After a session, the GM uses Distribute Rewards on the adventure to give currency to everyone who played. For anything else, such as a bonus or a penalty for one character, a GM can adjust the amount on the character's page.
A currency can count anything you want to track per character, for example:
Players spend their currency in the community's marketplaces between adventures. Every purchase is logged on the character's page, so a GM can check where an item came from. The player adds the item to their character sheet, which stays the record of what the character owns.
A price can be in experience as well as currency. A negative price gives the player that amount instead of taking it, which lets you set up exchanges, such as trading downtime points for gold or XP.
A reset sets one currency to the same amount for every character, on a schedule you choose. Use it to give every character the same downtime points to spend in a downtime marketplace, or to reset an event currency for a festival or the start of a new arc.