In an OUTER join, a condition in ON filters the join; the same condition in WHERE filters the result — different meaning.

The two clauses run at different moments. ON runs during matching — a failed condition just means 'no partner row', and the outer join keeps the left row anyway. WHERE runs after — and for the partnerless rows every right column is NULL, so a.term = 'spring' is UNKNOWN and the row dies. Same text, different clause, different question answered.

SELECT
  m.member
FROM
  members m
  LEFT JOIN attendance a ON a.member = m.member
WHERE
  a.term = 'spring'
ORDER BY
  m.member;

SELECT
  m.member
FROM
  members m
  LEFT JOIN attendance a ON a.member = m.member
  AND a.term = 'spring'
ORDER BY
  m.member;

New choir members with no spring attendance vanished from the roster — the term filter in WHERE deleted the NULL-extended rows and turned the LEFT JOIN inner.

Put right-table filters into ON to keep the outer rows, or accept the inner semantics and write INNER JOIN so the query says so.