This verb is also written in katakana despite the presence of kanjis. What is the difference between them ? In which context 嵌まる suits more than 填まる, what is the nuance ?
At the kanji level, 嵌 is not in the joyo kanji list, and it primarily means "inlay" or "pit(fall)". 填 is a variation of a joyo kanji 塡, but the reading of は-まる is not listed in the joyo kanji list. It mainly means "fill (a container, hole, etc)" or "compensate".
Both 填まる and 嵌まる are relatively difficult readings, although I believe most adults can read them. When people use はまる slangily in the sense of "to be trapped" or "to be stuck", it is almost always written as ハマる or はまる. When I need to choose a kanji, probably I prefer 嵌まる.
- ハマる: 83 results
- 嵌まる: 5 results (excluding 当て嵌まる)
- 填まる/塡まる: 1 result (!)
- Do not use 嵌まる/塡まる/填まる/ハマる whatsoever if you are writing something in "proper standard Japanese" (official document, magazine article, cooperate website, ...). Just use はまる.
- You can safely use ハマる in informal settings (online chat, blog) if it means "trapped", "stuck" or "addicted" (罠にハマった, この試験問題でハマった, サッカーにハマった).
- You may use the kanji versions in creative/stylistic writings (novel, poem, lyrics), but use 塡/填 only in fairly pompous/stiff ones. In the nature of creative writings, they are not strictly distinguished, but IMHO 嵌 tends to be chosen if it means "trapped" or "stuck", whereas 塡/填 tends to be chosen if it means "embedded" or "attached". (罠に嵌まった, この試験問題で嵌まった, 宝石が填まった石碑, 鉄の輪が填まった棒)
Bottom line is that most native speakers (including me) virtually have no reason to choose any of the kanji versions.
There is no difference. According to the dictionary they mean the same thing.