In my understanding, these two words breach and leak are used interchangeably in the security and privacy ecosystem. Professionals or researchers commonly use these words in their communication. Henceforth information/data breach or information/data leak means the information is accessible to an unauthorized or the confidentiality of the data is lost.
It is more important to understand other terms like events, incidents, and breaches.
Event: any observable happening, occurrence, or change in the normal state of a network, service, or system.
Incident: any event which leads to the compromise of confidentiality, integrity, and availability or violation of organization implemented controls (administrative, technical and physical)
Breach: A breach is, generally, unauthorized use or disclosure of protected health information (PHI), personally identifiable information (PII), Sensitive Information, etc.
A breach will always be an incident, while the incident doesn't need to be a breach.
Different security and privacy frameworks like ISO 27001, HIPAA, NIST, PCI-DSS, etc. have defined these terms.