What is the difference between a mora and a syllable?

Moras, known as haku (拍) in Japanese, are rhythmic units.^[1] The Japanese writing system of kana is based on moras, placing one kana on each mora. These are subtly different from syllables. Japanese forms of poetry based on "syllable counts" such as haiku (俳句), poems with seventeen "syllables", are not really based on counts of syllables, but on counts of moras.

Moras are very similar to syllables, but there are some differences.

A long vowel is counted as one syllable, but two moras. For example, aa is one syllable, but two moras, a-a, ou is one syllable, but two moras, o-o, and ei is one syllable, but two moras, e-e.
A syllabic n (ん) (see What is syllabic n?) is counted as one mora. For example, An is one syllable, but two moras, a-n', and kankei (関係), "relationship" is two syllables, "kan" and "kei", but four moras, ka-n'-ke-e.
Double consonants (sokuon) are counted as one mora. Thus oppai, "breasts" is two syllables, "op"-"pai", but four moras, o-(p holding)-pa-i, and similarly ippai (一杯) is two syllables, "ip"-"pai" but four moras, i-(p holding)-pa-i.
The Japanese phonetic system doesn't have any consonant terminated moras except n'. They do exist in practice, like the ending -des' for desu, but it is considered to have a (neutral or half) vowel of /u/. See also What is a devoiced vowel?

Similarly Tōkyō (東京) "Tokyo" and hanbun (半分), "half", can both be considered two-syllable but four-mora words.

Moras are counted as 1-paku, 2-haku, ... using haku (拍) or 1-on, 2-on, ... using on (音). See What is the counter for ...? for more on Japanese counting words.

Acknowledgements

This answer is based on a newsgroup post by muchan.

References

David Crystal, A Dictionary of Linguistics and Phonetics, page 312.; 2008

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