Season means two different things in anime. In Japanese scheduling it is the three-month broadcast quarter (winter, spring, summer, fall) in which a series airs. In Western usage it is a numbered production run of a series, like "season 2," regardless of when it aired.
The confusion is baked into the industry. In Japan, a season is the calendar quarter a series airs in: fans and databases sort new releases into the winter, spring, summer, and fall seasons, and a series' season usually means when it started. In English-language usage, a season is the release unit itself, the way it is for Western television, so Season 2 means the second production run whenever it aired.
The two meanings collide constantly. A Japanese two-cour series is one Western season but two Japanese seasons. A split-cour series may be sold as one season abroad while its home audience watched it across two different years. Streaming platforms have settled most arguments by simply numbering what they release, but their numbering reflects licensing bundles, not production.
Careful writers dodge the word or qualify it. On this site, season means the broadcast quarter when discussing Japanese scheduling and the numbered production run when discussing a specific series' structure, and the distinction is printed wherever it could change an answer. Release calendars published each quarter use the Japanese meaning, listing every new series under its start season, which is why chart sites and Western episode numbering so often seem to disagree.
In use"The show's second season began in the fall season: both meanings, one sentence apart."