fortlaufend
continuous
Continuing or taking place without interruption; continuous.
Die Software wird fortlaufend aktualisiert, um Sicherheitslücken zu schließen.
The software is continuously updated to close security gaps.

continuous / consecutive
Loading your saved state.
continuous
Continuing or taking place without interruption; continuous.
Die Software wird fortlaufend aktualisiert, um Sicherheitslücken zu schließen.
The software is continuously updated to close security gaps.

'Fortlaufend' (continuous/consecutive) is the present participle of the verb 'fortlaufen' (fort + laufen). The literal meaning 'running onward' helps you understand both meanings: a process that keeps 'running on' over time, or numbering that 'continues' in sequence.
Die Geschichte wird fortlaufend erzählt.
The story is told continuously.
'Fortlaufend' (continuous/consecutive) can be used as an adjective before a noun or as an adverb that describes a verb. Its position in the sentence changes, but the form of the word does not.
Für die Umfrage brauchen wir eine fortlaufende Nummerierung.
For the survey, we need consecutive numbering.
You can recognize the meaning 'in einer Reihenfolge' (in a sequence) by the fact that it refers to countable things such as numbers, pages, volumes, or codes. In this case, it is always about an ordered sequence.
Die Rechnungen müssen fortlaufend archiviert werden.
The invoices must be archived consecutively.
In the meaning 'kontinuierlich' (continuously), 'fortlaufend' is often used with verbs that describe a process. Typical combinations are 'fortlaufend verbessern' (to continuously improve), 'fortlaufend überwachen' (to continuously monitor), or 'fortlaufend anpassen' (to continuously adapt).
Die Qualität unserer Produkte wird fortlaufend kontrolliert.
The quality of our products is continuously checked.
constant
'ständig' and 'fortlaufend' can both mean that something happens without interruption or again and again. 'ständig' sounds very natural in everyday language and is often used for frequent actions, problems, or habits. It can also sound somewhat annoyed. 'fortlaufend' is more suitable for a process that continues in an organized way, for example with reports, courses, or payments. In addition, 'fortlaufend' can refer to a sequence, such as 'fortlaufende Nummern' (consecutive numbers). The words can be confused when talking about duration. As a simple guide: for everyday situations and frequency, you often use 'ständig'; for an ongoing process or a series, 'fortlaufend' is more likely.

Im Verein werden die Ausgaben fortlaufend in einer Liste notiert.
At the club, the expenses are continuously recorded in a list.
Meine Schwester hat beim Einkaufen ständig ihr Handy gesucht.
My sister kept looking for her phone while shopping.