Insolvency is the state of being unable to pay the debts, by a person or company (debtor), at maturity; those in a state of insolvency are said to be insolvent. There are two forms: cash-flow insolvency and balance-sheet insolvency.
Cash-flow insolvency is when a person or company has enough assets to pay what is owed, but does not have the appropriate form of payment. For example, a person may own a large house and a valuable car, but not have enough liquid assets to pay a debt when it falls due. Cash-flow insolvency can usually be resolved by negotiation. For example, the bill collector may wait until the car is sold and the debtor agrees to pay a penalty.
Balance-sheet insolvency is when a person or company does not have enough assets to pay all of their debts. The person or company might enter bankruptcy, but not necessarily. Once a loss is accepted by all parties, negotiation is often able to resolve the situation without bankruptcy.
A company that is balance-sheet insolvent may still have enough cash to pay its next bill on time. However, most laws will not let the company pay that bill unless it will directly help all their creditors. For example, an insolvent farmer may be allowed to hire people to help harvest the crop, because not harvesting and selling the crop would be even worse for his creditors.
It has been suggested that the speaker or writer should either say technical insolvency or actual insolvency in order to always be clear - where technical insolvency is a synonym for balance sheet insolvency, which means that its liabilities are greater than its assets, and actual insolvency is a synonym for the first definition of insolvency ("Insolvency is the inability of a debtor to pay their debt.").
While technical insolvency is a synonym for balance-sheet insolvency, cash-flow insolvency and actual insolvency are not synonyms. The term "cash-flow insolvent" carries a strong (but perhaps not absolute) connotation that the debtor is balance-sheet solvent, whereas the term "actually insolvent" does not.