The same design principle, applied a thousand years apart
Katakana and hiragana were derived from Chinese characters in the 9th century: katakana from fragments of characters (ア from 阿, カ from 加), hiragana from their cursive full forms (あ from 安, か from 加). The character kept its sound and lost its meaning, reduced to a few strokes.
Zhuyin was built the same way, just thirteen centuries later. In 1913, a Republic of China commission took existing Chinese characters, one per sound, and cut each down to a simplified fragment (the source character behind all 37 symbols is documented here). ㄅ comes from 勹. ㄖ comes from 日. The method is identical to the one that produced kana. This is not a loose resemblance between two old writing systems. It is the same solution to the same problem, reached independently, a thousand years apart.
Both separate sound from meaning the same way, on the page
In a Japanese children’s book, kanji carry meaning and furigana printed beside them carry the sound, for a reader who cannot yet recognize the kanji alone. In a Taiwanese children’s book, Chinese characters carry meaning and zhuyin printed beside them carries the sound, for exactly the same reason (this is covered in detail in the guide for parents in Taiwan).
This is not a metaphor to help the comparison land. It is the same page layout, the same pedagogical logic, and in Taiwan’s case, a system that was explicitly designed with the kana precedent already in mind. A Japanese reader does not need furigana explained. Reading a zhuyin-annotated Chinese sentence is the same visual habit already built from a lifetime of reading kanji with furigana attached.
Where the resemblance ends: kana is a syllabary, zhuyin is not
Here is the real structural difference, and it matters more than the shared ancestry. Kana is a syllabary: か is one indivisible unit for "ka", not a k-symbol plus an a-symbol. You cannot split it apart in the writing system, because Japanese does not need to; its syllable shapes are simple and limited.
Zhuyin does the opposite. A Mandarin syllable is built from up to three pieces, an initial, a medial and a final, each with its own symbol, plus a tone mark on top (the full breakdown is here). ㄒㄧㄢ for xiān is three separate symbols in a column, not one block standing for the whole syllable. Mandarin syllables are simply more complex than Japanese morae, so the writing system that fits them has to decompose further than kana ever needs to.
The practical effect for a Japanese speaker: the concept, a small phonetic set standing in for sound alone, needs no introduction. The internal structure does. Expect the first hour with zhuyin to feel like learning a new kind of kana rather than a new kana chart.
Tones: the one piece with no equivalent in the kana system
Japanese has pitch accent, a rise or fall in pitch that can distinguish words like 箸 (hashi, chopsticks) from 橋 (hashi, bridge). It is real, and it means the underlying idea, that pitch changes meaning, is not foreign to a Japanese speaker the way it can be to an English one.
It is not the same system, though, and it will not transfer automatically. Mandarin marks a specific tone on every single syllable, from a fixed set of five, and getting it wrong changes the word, not just the nuance. Practicing tones deliberately from the start matters regardless of what your first language already does with pitch.
A quieter advantage: the vowels and the syllable shapes
Japanese has five clean vowels, a, i, u, e, o, that land close to their zhuyin equivalents. English vowels, by comparison, are a mess of diphthongs and regional drift that constantly mislead English-speaking learners into hearing sounds that are not there.
Japanese syllables are also simple: essentially consonant plus vowel, with no consonant clusters. Mandarin syllables are more complex than that, but they are still far closer to Japanese’s clean CV shape than to English’s "strengths"-style clusters. A Japanese speaker is not fighting the urge to jam extra consonants into a Mandarin syllable the way learners from cluster-heavy languages often are.
None of this makes Mandarin pronunciation automatic for a Japanese speaker. It means several of the specific habits that trip up other learners, unfamiliar vowels, consonant clusters, a totally new idea of what a phonetic script is for, are not obstacles you are starting from zero on.
Where to start
Treat zhuyin as new symbols mapped onto a system you already understand, not a new system to understand. The two-hour guide covers all 37 symbols in the order that sticks best, the interactive chart lets you hear each one against native audio rather than guessing from a description, and the app turns the recognition drilling into something closer to how kana itself was originally memorized, through repetition, not explanation.