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.

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?
today
'heute' and 'heutig' are closely related, but they are used differently grammatically. 'heute' is an adverb: it says when something happens, namely on this day or in the present day. 'heutig' is an adjective: it stands with a noun and means 'of today' or 'belonging to the present day'. The confusion arises because both have the same time reference. In practice: with a verb, you usually use 'heute'; with a noun, often 'heutig', for example 'die heutige Sitzung' (today's meeting).

Nach der heutigen Besprechung weiß das Team, was bis Freitag zu tun ist.
After today's meeting, the team knows what needs to be done by Friday.
Sie lernt heute noch für die Prüfung, weil sie morgen früh schreiben muss.
She is still studying for the exam today because she has to take it early tomorrow.