heute
today
Refers to the current day, that is, the day on which one is speaking or writing.
Heute scheint die Sonne.
The sun is shining today.

today
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today
Refers to the current day, that is, the day on which one is speaking or writing.
Heute scheint die Sonne.
The sun is shining today.

When 'heute' stands at the beginning of the sentence (position 1), the conjugated verb follows directly in position 2, and the subject comes only after that. This switch is called inversion.
Heute habe ich viel zu tun.
Today I have a lot to do.
To name a specific part of the day, 'heute' is combined with times of day. You say 'heute Morgen' (this morning), 'heute Mittag' (today at noon), and 'heute Abend' (this evening), but 'heute Nacht' (tonight/last night).
Ich gehe heute Abend ins Kino.
I'm going to the movies this evening.
The adjective 'heutig' is derived from the adverb 'heute'. It means 'of today' or 'present-day' and is declined before a noun.
Die heutige Jugend hat andere Interessen als frühere Generationen.
Today's youth have different interests from earlier generations.
The meaning 'heutzutage' (nowadays) can often be recognized by the fact that a comparison with the past is being made. Sometimes the word 'früher' (in the past / formerly) appears in the same or a nearby sentence.
Früher schrieb man Briefe, heute schickt man E-Mails.
In the past people wrote letters; today they send emails.
now
'jetzt' and 'heute' both talk about the present. 'jetzt' usually means this moment or the current time right now. 'heute' means the whole day on which you are speaking. In a broader sense, both can also mean the present day or current era, that is, the present in contrast to the past. They are easy to confuse because both often have to do with the present. As a practical rule: use 'jetzt' for the exact moment, and 'heute' for the current day.

Heute arbeiten wir in der Werkstatt an dem neuen Projekt.
Today we are working on the new project in the workshop.
Sie kann jetzt nicht sprechen, weil sie im Meeting ist.
She can't talk right now because she is in a meeting.