1. "病人" is a term that has existed in the Chinese language for over 2000 years. It is widely used and understood. 2. "患者" is a much younger noun derived from the verb "患" - "suffer from" - and is often used with an object, which is the illness. Suffering from what? Tuberculosis, for example. 肺结核患者。So "患者" is used when a specific illness is mentioned. So we use "心脏病患者" much more than "心脏病病人". A more often used derivative of 患 is 患处， meaning "the affected area". Example, 把药膏涂在患处， 一天三次。患者follows the same logic of derivation: it is the person affected by the ailment. In a lecture on a specific ailment, the lecturer would normally use 患者、患处。例: 患者应该注意把患处保持干爽，以免发炎。 3. In a hospital, you will hear nurses and doctors say "病人在哪里?" "帮病人量血压"， and not "患者在哪里?" "帮患者量血压". 4. 病人 thus is a more generic term. 患者 leads the reader immediately to the thought of "Which ailment are you talking about? 什么病的患者?" 5. "隐形病患者" we don't immediately perceive as a "病人"。 他看起来很健康，不像病人，原来却是高血压患者。 So you see the differences between the two terms. 6. To use 患者 as an exact synonym of 病人 is a recent practice. It is often used in academic jargon. 医患关系 - doctor-patient relations - is jargon that is often heard nowadays, as it is a major socio-economic problem. The rise of 患者 as a synonym or even replacement of 病人 may be due to the increasing awareness and frequent discussion of 医患关系. 患者 has become more of a word of "top-of-mind recall" than before. 7. It would be silly to think that 患者 is a more formal noun.

病人 病患 患者 are mutually replaceable.

患者 more officially than 病人 to used in public way like TV or notification. 病人 usually used in oral way.

病人=患者。Only patients is a professional term。

The two words are same meaning. In China, there is a word 医患, it means doctor and patient.