These terms are loosely defined. They have alternate terms in different settings, and the same term can mean slightly different things. In general, they refer more or less to the same thing.
Patient notes are sometimes called "progress notes", or "patient record", or other terms. They are notes concerning a single patient, compiled or written by one or more clinicians.
Clinical notes are sometimes called "hospital notes", or "clinical record", or other terms. They can refer to a single patient or something broader, even a general topic. They are compiled or written by one or more clinicians.
Clinician notes are sometimes called "clinical notes", "progress notes", "clinical case notes", and other terms. "Clinician" implies that they are the notes of a single clinician. They typically concern a single patient, but depending on the setting, they could refer to something broader.
"Clinician" applies to a healthcare professional who is a primary care giver for a human patient (rather than specializing in laboratory or research techniques).