
heutig
today's
Refers to the current day, that is, 'of today'.
Die heutige Ausgabe der Zeitung liegt schon auf dem Tisch.
Today's edition of the newspaper is already on the table.
today's / present-day
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today's
Refers to the current day, that is, 'of today'.
Die heutige Ausgabe der Zeitung liegt schon auf dem Tisch.
Today's edition of the newspaper is already on the table.

present-day
Refers to the present or the current time in general; contemporary.
Aus heutiger Sicht ist diese alte Technologie kaum noch vorstellbar.
From today's perspective, this old technology is hardly imaginable anymore.
The adjective 'heutig' is derived from the adverb 'heute' (today) by adding the ending '-ig'. This pattern is also found with other adverbs of time and place, e.g. 'gestern' → 'gestrig' (yesterday's) or 'dort' → 'dortig' (local/there).
Die gestrige Feier war ein großer Erfolg.
Yesterday's party was a great success.
'Heutig' is used almost exclusively as an attributive adjective, meaning it stands directly before a noun and is declined. It is not used as a standalone predicate.
Das heutige Wetter ist sehr schön.
Today's weather is very nice.
Common combinations are 'der heutige Tag' (today), 'das heutige Datum' (today's date), or 'das heutige Treffen' (today's meeting) when referring to the specific day. In a more general meaning, you find it in 'aus heutiger Sicht' (from today's perspective) or 'die heutige Gesellschaft' (today's society).
Was ist das heutige Datum?
What is today's date?
current
Both words can refer to the present. Heutig mainly refers to the current day or the present time, while aktuell additionally emphasizes that something is currently relevant, interesting, or up to date. Heutig fits a simple date reference, while aktuell is more suitable for important information about the present.

Die heutige Meldung erscheint wie geplant am Morgen.
Today's report will be published in the morning as planned.
Die aktuelle Meldung informiert uns über die wichtigen Ereignisse des Tages.
The current report informs us about the day's important events.