There is one word, あげる, and it has many meanings. It can be written in several different ways. You would find all of these meanings and ways of writing them under one entry in a monolingual dictionary. Jisho is just set up to display one way of presenting it in kanji in the header, but that is never meant to be a suggestion that it is the "main" way or anything. The individual meanings all have their specific notes for if they are usually written with a particular kanji or with no kanji, etc.
I see, Thanks @Leebo! I thought it was more like the Kanji determined whether it was a separate word or not, not the pronunciation. The more you know!
Hmm, actually, about that. Why isn't Kami listed as one word then? https://jisho.org/search/kami
Those are all different words that just happen to be pronounced "kami." It's a different situation. In the case of "ageru" it is one word with many meanings. Linguists can tell this kind of thing from how the words developed over time. Also, not all of the "kami" words have the same pronunciation.
髪 and 紙 are kaMI but 神 is KAmi. Different pitch accents.
To elaborate further, 神 comes from Proto-Japonic kamuy
Source: https://en.wiktionary.org/wiki/%E7%A5%9E
髪 possible was derived from 上 (also pronounced kami) as in hair "on top" of your head or from 頭身毛 head/body/hair
Source: http://gogen-allguide.com/ka/kami_hair.html#:~:text=%E9%AB%AA%E3%81%AE%E8%AA%9E%E6%BA%90%E3%81%AF%E3%80%81%E3%80%8C%E4%B8%8A,%E3%81%AB%E7%94%B1%E6%9D%A5%E3%81%99%E3%82%8B%E3%81%A8%E3%81%97%E3%81%A6%E3%81%84%E3%82%8B%E3%80%82
紙 possibly comes from 木簡 (mokkan) where the kan part morphed over time from kan to kani to kami.
Source: https://dtp-bbs.com/road-to-the-paper/column/column-090.html#:~:text=%E3%80%8C%E7%B4%99%E3%80%8D%E3%81%AE%E8%A8%93%E8%AA%AD%E3%81%AF%E3%80%8C,%E3%81%A8%E6%8E%A8%E5%AF%9F%E3%81%95%E3%82%8C%E3%81%A6%E3%81%84%E3%81%BE%E3%81%99%E3%80%82
Also, remember that Japanese was a spoken language with no writing before kanji were imported from China. They borrowed many Chinese pronunciations and adapted them to the Japanese pronunciation scheme (on'yomi). They also assigned kanji to existing Japanese words and expressed nuances with different kanji. So while あげる (to raise) and あげる (to fry) come from the same original word, the different usages can be expressed with different kanji to make things clearer for a reader.
Awesome, thank you very much for sharing!
Aren't these 4 different words
If I write "この本をあげる", it has a different meaning to "この本を上げる/挙げる/揚げる". So aren't all 4 of these different words instead of all stemming from 上げる but with 27 different meanings?