
universell
universal
Generally valid, applicable or relevant to everyone and everywhere.
Die Sprache der Musik ist universell und wird auf der ganzen Welt verstanden.
The language of music is universal and is understood all over the world.
universal
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universal
Generally valid, applicable or relevant to everyone and everywhere.
Die Sprache der Musik ist universell und wird auf der ganzen Welt verstanden.
The language of music is universal and is understood all over the world.

versatile
Usable in many ways or suitable for various purposes.
Dieses Schweizer Taschenmesser ist ein universelles Werkzeug für unterwegs.
This Swiss Army knife is a versatile tool for when you're on the go.
'Universell' (universal) is related to 'Universum' (universe) and 'Universität' (university). The shared root points to the idea of 'totality' or 'all-encompassing'. So a universal law applies to everyone, and a universal tool can be used for everything.
Die Gesetze der Physik sind universell.
The laws of physics are universal.
You can recognize the meaning from the noun. In connection with abstract concepts like 'Rechte' (rights), 'Werte' (values), or 'Sprache' (language), 'universell' means something like 'universally valid'. In connection with concrete objects like 'Werkzeug' (tool) or 'Adapter' (adapter), it means 'versatile' or 'usable in many ways'.
Menschenrechte sollten universell sein.
Human rights should be universal.
A very common and useful combination is 'universell einsetzbar' (usable in many ways / universally applicable). This phrase describes that something can be used for many different purposes or in many situations.
Diese Software ist flexibel und universell einsetzbar.
This software is flexible and versatile.
versatile
Both words can indicate that something is suitable for different purposes. Vielseitig (versatile) lists several different possible uses, while universell (universal) emphasizes exceptionally broad usability for almost all suitable cases. Use vielseitig when stressing great variety, and universell when the validity or use is meant to be very comprehensive.

Der universelle Adapter eignet sich für fast alle Geräte in unserem Haushalt.
The universal adapter works with almost all the devices in our household.
Das vielseitige Gerät eignet sich für die Arbeit, für Reisen und für den Sport.
The versatile device is suitable for work, travel, and sports.