If I have to pay an invoice it's my liability. If someone has to pay an invoice issued by me it's also liability. Are there any words that distinguish these two types of liabilities?
Disclaimer: Sorry if that's obvious, I'm not a native speaker.
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They are the same sort of liability, so there is no need for a term to distinguish them.
However, they are not both liabilities on the same set of books. The invoice you must pay is a liability (a payable) on your books, but an asset (a receivable) on your customer's books. Likewise, the invoice your customer must pay you is an asset (a receivable) on your books, and a liability (a payable) only on your customer's books.