I don't see any reason why these tags wouldn't be used interchangeably.
To put the alternate case to Nathan's answer, I propose we keep billing.
My reasons because it's more used than bills, which suggests that it's what our users find more natural on average.
EDIT: I've now done this. In doing so I noticed a few questions where the topic was really "paper money". I've removed the tag from those and replaced it with cash. It's a usage specific to American English anyway.
My preference if we merge would be to keep bills, because billing is less of a personal finance topic and more of an accounting topic. From the consumer's perspective, they are receiving a bill. They're two sides of that same coin. I prefer that we keep the focus on the consumer's perspective in that exchange.