
laufend
ongoing
Describes something that is currently taking place, is current, or is continuing.
Die laufenden Kosten für das Projekt sind höher als erwartet.
The ongoing costs for the project are higher than expected.
ongoing / continual
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ongoing
Describes something that is currently taking place, is current, or is continuing.
Die laufenden Kosten für das Projekt sind höher als erwartet.
The ongoing costs for the project are higher than expected.

continual
Means that something happens constantly, continuously, or in rapid succession.
Wir erhalten laufend neue Anfragen von Kunden.
We are continually receiving new inquiries from customers.

running
Describes something that is in a flowing motion, especially water.
Für das Rezept benötigen Sie einen halben Liter laufendes Wasser.
For the recipe, you need half a liter of running water.
The word 'laufend' is the present participle of the verb 'laufen' (to run/walk). It describes that something is currently active or continuing, similar to a person who is currently running. This form is often used as an adjective before a noun.
Die laufende Ausstellung im Museum ist sehr beliebt.
The ongoing exhibition at the museum is very popular.
In the meaning of 'current/ongoing', 'laufend' is often used in business or organizational contexts. Typical combinations are 'laufende Kosten' (ongoing costs), 'ein laufendes Projekt' (an ongoing project), or 'das laufende Geschäftsjahr' (the current fiscal year).
Bitte informieren Sie mich über den laufenden Stand des Projekts.
Please inform me about the current status of the project.
In the meaning of 'constantly/continually', 'laufend' is often used as an adverb that describes the frequency of an action. It can stand in different positions in the sentence, often directly after the verb or at the beginning of the sentence for emphasis.
Wir bekommen laufend neue E-Mails.
We are continually getting new emails.
When 'laufend' describes physical movement, it almost always refers to 'laufendes Wasser' (running water) from a tap. This word combination is very fixed and a clear signal for this meaning.
Waschen Sie das Gemüse bitte unter laufendem Wasser.
Please wash the vegetables under running water.
current
„Aktuell“ and „laufend“ can both be used for something important that is currently underway. „Aktuell“ highlights its present significance or the current state of the information, while „laufend“ indicates that a process is taking place and is still continuing. „Aktuell“ fits when talking about relevance; „laufend“ is more suitable when describing the course of a process.

Das laufende Projekt soll erst im nächsten Monat fertig werden.
The ongoing project is not expected to be finished until next month.
Das aktuelle Projekt ist für unsere Abteilung besonders wichtig.
The current project is particularly important to our department.