
gültig
valid
Officially recognized and effective for a certain period of time or under certain conditions.
Dieses Ticket ist nur heute gültig.
This ticket is only valid today.
valid
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valid
Officially recognized and effective for a certain period of time or under certain conditions.
Dieses Ticket ist nur heute gültig.
This ticket is only valid today.

valid / applicable
Relevant or applicable; in effect for someone or something.
Die neue Hausordnung ist für alle Mieter gültig.
The new house rules are valid for all tenants.
Careful, 'gültig' (valid) is a false friend! It means 'valid' in English, not 'guilty'. The English word 'guilty' is translated into German as 'schuldig'.
Mein Fahrschein ist leider nicht mehr gültig.
Unfortunately, my ticket is no longer valid.
'Gültig' (valid) is the adjective related to the strong verb 'gelten' (to be valid/apply). The sentences 'Das Ticket ist gültig' (The ticket is valid) and 'Das Ticket gilt' (The ticket is valid/applies) have a very similar meaning.
Diese Eintrittskarte gilt für zwei Personen.
This admission ticket is valid for two people.
In connection with official validity, 'gültig' (valid) is often combined with a time expression. Typical patterns are 'gültig bis [Datum]' (valid until [date]) or 'gültig für [Zeitraum]' (valid for [period of time]). It is often used for documents such as tickets, passports, or contracts.
Das Angebot ist nur bis Ende des Monats gültig.
The offer is only valid until the end of the month.
When 'gültig' (valid/applicable) means that something applies or is applicable, it is often followed by the preposition 'für' with the accusative. This limits the scope of validity, for example to a group of people.
Die neue Regelung ist für alle Mitarbeiter gültig.
The new regulation is valid for all employees.
active
For a card or membership, both words can mean that it can currently be used. „Aktiv“ describes an enabled or currently operating status; „gültig“ emphasizes that it is officially recognized and that the conditions or period of validity still apply. Depending on the intended nuance, both words are possible.

Die Kundenkarte ist noch bis Ende des Monats gültig und kann benutzt werden.
The customer card is still valid until the end of the month and can be used.
Die Kundenkarte ist nach der Anmeldung sofort aktiv und kann benutzt werden.
The customer card is active immediately after registration and can be used.