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PENALTY, contr. A clause in an agreement, by which the obligor agrees to pay a certain sum of money, if he shall fail to fulfill the contract contained in another clause of the same agreement. (A Law Dictionary, Adapted to the Constitution and Laws of the United States. By John Bouvier.)

Liquidated damages (also referred to as liquidated and ascertained damages) are damages whose amount the parties designate during the formation of a contract for the injured party to collect as compensation upon a specific breach (e.g., late performance). [...] At common law, a liquidated damages clause will not be enforced if its purpose is to punish the wrongdoer/party in breach rather than to compensate the injured party (in which case it is referred to as a penal or penalty clause). (Wikipedia)

In the United States, a liquidated damage clause is intended to estimate damages in the event of non-performance or breach of contract. [...] The intent of liquidated damages is simply to measure damages that are hard to prove once incurred. If the liquidated damages are disproportionate, they can, however, be declared a penalty. The clause is then void, and recovery will be limited to the actual damage that results from the breach. [...]

In civil law countries, the attitude toward contractual penalties is quite different from the common law approach. The Napoleonic Code, upon which most civil codes are based, allowed for penalties to encourage performance of contractual obligations. (This is the precise rationale that is rejected in the United States.) (lexology.com)