だ / です

1. 1Polite copula identifying or describing the topic, like 'is/am/are'.Ex. 1
2. 2Plain copula stating that something is a certain thing or in a certain state, used in casual or plain-style contexts.Ex. 2
3. 3です added after an い-adjective to make the sentence polite.

です is the default polite form for speaking to strangers, teachers, or in service settings. だ is used with friends and family and in plain-style writing such as diaries or essays. Both state what something is or what state it is in, and speakers usually keep one style consistently within a conversation or text.

• 〜は〜ですN5「〜は〜です」is a complete polite sentence pattern that marks the topic with「は」and then makes a judgment with「です」;「だ / です」are just sentence-final judgment copulas, with the plain form「だ」, and can also be used in sentences without「は」.
• 〜は〜ではありませんN5「〜は〜ではありません」is the polite negative form of「です」, meaning "A is not B"; it attaches to nouns and な-adjective stems but not い-adjectives (say「高くないです」instead). The negative of「だ」is「ではない」.
• でしょうN5「だ / です」express a definitive assertion, while「でしょう」expresses conjecture ("probably...") or rising-intonation confirmation ("...right?"), with a softer tone.「でしょう」can attach directly to the plain form of verbs, and after nouns and な-adjectives it drops「だ」.
• だろうN5「だ / です」make a clear assertion of "is...", whereas「だろう」expresses conjecture ("probably...") or seeks confirmation with rising intonation; the two are not interchangeable.「だろう」can also attach directly to the plain forms of verbs and い-adjectives, and its polite equivalent is「でしょう」.
• でございますN4「でございます」is more formal than「です」, used mainly in service settings such as shops and hotels; it can replace「です」after nouns and な-adjectives, but it cannot attach directly to い-adjectives and is not used to state the listener's own identity.

〜は〜です is the basic sentence frame built on です, and 〜は〜ではありません is its polite negative. でしょう and だろう are the conjectural ('probably is') forms of です and だ, while でございます is a more formal, deferential equivalent of です.