Although desistimiento generically denotes “withdrawal” or “abandonment,” the appropriate translation of the term depends on the area of legal practice in which it is used. In criminal law, in the context of defining “criminal attempt” (tentativa de delito), desistimiento de la tentativa refers to a criminal perpetrator’s voluntary abandonment of or withdrawal from a crime before it is consummated (desistimiento voluntario antes de consumar el delito). In English this is often formally called “renunciation of criminal purpose.”
In contract law desistimiento de contrato likewise denotes the voluntary, often unilateral withdrawal from a contract (desistimiento unilateral), and in English this may be expressed as a “unilateral cancellation (or) termination of contract.” Likewise, the right to withdraw from or to unilaterally terminate a contract and cancel a purchase (called derecho de desistimiento) is a feature of Spanish consumer protection legislation (Real Decreto Legislativo 1/2007, por el que se aprueba el texto refundido de la Ley General para la defensa de los consumidores y usuarios).
In other contexts, desistimiento (del demandante) is likewise used in civil procedure to denote the plaintiff’s abandonment of a proceeding before a trial of the issues, which does not preclude future prosecution of the claim (declaración unilateral del actor por la que tiene por abandonado el proceso, sin que ello suponga renuncia a la acción). In many US jurisdictions this “abandonment of suit” is known as a “voluntary dismissal” of the action or claim.
For the difference between desistimiento and renuncia in civil proceedings see: https://rebeccajowers.com/2016/07/26/espanol-juridico-8/