
gegenwärtig
current
Current or taking place in the present time; what exists now. Used as an adjective.
Die gegenwärtige politische Lage in Europa ist sehr angespannt.
The current political situation in Europe is very tense.
current / present
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current
Current or taking place in the present time; what exists now. Used as an adjective.
Die gegenwärtige politische Lage in Europa ist sehr angespannt.
The current political situation in Europe is very tense.

currently
Used as an adverb to express that something is happening at present or at the moment. Synonymous with 'momentan' (at the moment) or 'derzeit' (currently).
Gegenwärtig arbeiten wir an der Fertigstellung des Berichts.
Currently, we are working on completing the report.

to be present
To be mentally present, attentive, and focused on what is happening.
Obwohl er im Raum saß, war er mit seinen Gedanken nicht wirklich gegenwärtig.
Although he was sitting in the room, he was not really present in his thoughts.
'Gegenwärtig' (current/present) is the adjective related to the noun 'die Gegenwart' (the present), which means 'the present time' or 'presence'. This connection helps you understand the main meanings.
Wir müssen uns auf die Probleme der Gegenwart konzentrieren.
We need to focus on the problems of the present.
'Gegenwärtig' (current/currently) can be used as an adjective before a noun or as an adverb. As an adjective, it is declined ('die gegenwärtige Situation' — the current situation). As an adverb, it remains unchanged and often stands at the beginning of the sentence, which triggers inversion ('Gegenwärtig haben wir...' — Currently we have...).
Die gegenwärtige Technik ermöglicht viele neue Dinge.
Current technology makes many new things possible.
As an adjective, 'gegenwärtig' (current) is often used in formal, official, or academic texts. It sounds more elevated than the word 'aktuell' (current/up-to-date).
Der Artikel analysiert die gegenwärtige Forschungslage.
The article analyzes the current state of research.
In the meaning 'geistig anwesend' (mentally present), 'gegenwärtig' (present) is almost always used with the verb 'sein' (to be), often in a negated form. It describes a person's state of attention.
Er hörte zwar zu, aber seine Gedanken waren nicht ganz gegenwärtig.
He was listening, but his thoughts were not completely present.
today
Heute and gegenwärtig can both describe a current situation. Heute usually refers to the current day. Gegenwärtig refers to a period around the present that is not precisely defined and usually sounds more formal, for example in factual communications.

Gegenwärtig sind in diesem Hotel keine Zimmer frei.
There are currently no rooms available at this hotel.
Heute sind in diesem Hotel keine Zimmer frei.
There are no rooms available at this hotel today.