I assume you mean that you send an invoice to the company that was not paid. In such an instance, the bill becomes an unpaid debt. If it is not paid by the date on which it is due and payable, then you can, indeed, sue to collect it. Your lawsuit would be for debt, a cause of action at law.
There are some complications. Your remedy if you were successful in court would be a judgment against the company. The judgment would be viable for ten years or more, dependent upon your jurisdiction, and would also earn interest at the legal rate until paid. You would have the right to execute on the judgement and have any assets of the company which owed you the money seized and sold to satisfy the debt. Still, some assets are exempt from execution, and the company may have no assets. Many businesses are set up as corporations in which the corporation has few or no assets as a means of protecting the assets of the principal. In that event, your chances of collecting your debt are problematic. You cannot imprison a person in the United States for debt unless that debt is for alimony or child support, nor can you garnish wages or seize bank accounts. Your judgment simply transforms your debt into a collectible enforceable debt, if it is in fact collectible.