The state of nirvana described is somewhat different in Jainism than the Buddha.
The Buddha’s concept of nibbana is the removal of raga, dosa, and moha.
Even before that it is a common term used by the general population as a word that refered to blowing out the fire. I guess back then there is no electricity, the use of candles /lamp is everywhere. The Buddha used it to refer to the blowing out ( extinguishing ) of a different type of fire: namely the fire of raga, dosa, and moha. Hence this common term generally used as extinguishing the fire ( of a lamp or candle) was used to explain the extinction of the three root defilement.
It is mentioned that " non-Buddhist texts, such as the Jain sources, the Yoga Sūtra of Patañjali and some later Upaniṣads (such as the Maitrī Upaniṣad), which contain similar terms cannot be dated earlier than the beginning of the Common Era (CE).43 In such cases, we can justifiably assume that they might have been the result of Buddhist influence, rather than the other way around."
The Buddha often used common language in the area to explain his teaching so it is easy for people of that region to understand /relate. For example, if a Chinese monk comes to the U.S. and teach the dhamma he wouldn't be teaching it in Chinese. The natural thing to do is to learn the language of the area and teach it using English terms that people are using already. If he use Chinese or a brand new language ( that people are unfamiliar with) , it wouldn't make any sense considering how difficult some concepts can be. So in this case the thing to do is try to explain the concept using words that people already understand , are familiar with, and are using in day to day life.