じゃない・ではない
is not
Noun / な-adjective + じゃない (polite: じゃありません / じゃないです)
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The negative of だ is じゃない: 学生じゃない, "(I'm) not a student". じゃ is a contraction of では, so ではない is the same thing in careful or written style.
For the polite negative there are two routes, and both are common:
- じゃありません, a little more formal
- じゃないです, very common in conversation
Each has a では version too (ではありません, ではないです).
じゃない works after nouns and な-adjectives. い-adjectives have their own negative, 高くない, which comes later. ない on its own means "there isn't", so the じゃ can't be dropped.
Register: じゃ is spoken; では is written or careful speech. Polite: じゃありません (a little more formal) or じゃないです (very common in speech).
Examples
私は先生じゃない。
I'm not a teacher.
これは私のかばんじゃありません。
This isn't my bag.
明日は日曜日じゃないよ。
Tomorrow isn't Sunday, you know.
あの人は日本人ではありません。
That person isn't Japanese.
それは田中さんの車じゃないです。
That's not Mr Tanaka's car.