Rishi [Hindi/Sanskrit:ऋषि] is an ascetic, who is devoted to religious activities. He is devoted to religious activities.
In ancient times Kings were guided by Rishis as Raaj Dharma was also considered a part of Dharma

Dharma

Dharma means Law or Natural Law and is a concept of central importance in Indian philosophy and religion. In the context of Hinduism, it refers to one's personal obligations, calling and duties, and a Hindu's dharma is affected by the person's age, caste, class, occupation, and gender...

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Rishi spent most of their life in forest. They were renounced persons. They were respected due to there knowledge of Dharma

Dharma

Dharma means Law or Natural Law and is a concept of central importance in Indian philosophy and religion. In the context of Hinduism, it refers to one's personal obligations, calling and duties, and a Hindu's dharma is affected by the person's age, caste, class, occupation, and gender...

 and there selflessness life.

Muni [Hindi/ Sankrit: मुनि] word is somewhat related to Rishi. A Rishi who performs devotion by keeping himself silent is called a Muni. Actually this is normally pronunced with Rushi as Rishi-Muni (ऋषि मुनि).
Different types of Rishis are mentioned in the Sanatan (Hindu Religious) literarure.