
variieren
to vary
To differ or occur in different forms or versions.
Die Preise für Hotelzimmer variieren stark je nach Saison.
The prices for hotel rooms vary greatly depending on the season.
to vary
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to vary
To differ or occur in different forms or versions.
Die Preise für Hotelzimmer variieren stark je nach Saison.
The prices for hotel rooms vary greatly depending on the season.

to vary
To intentionally change or modify something in order to create variety.
Sie können das Rezept variieren, indem Sie statt Mandeln Nüsse verwenden.
You can vary the recipe by using nuts instead of almonds.
Verbs ending in '-ieren' often come from other languages and are always regular. They form the past participle without 'ge-'. So it is 'hat variiert' (has varied).
Der Koch hat das klassische Rezept etwas variiert.
The cook varied the classic recipe a little.
'Variieren' can be used with or without an accusative object. Without an object, it means that things are different by themselves. With an object, it means that someone actively changes something.
Die Meinungen zu diesem Thema variieren stark.
Opinions on this topic vary greatly.
When something differs by itself, 'variieren' is often used with words such as 'Preise' (prices), 'Größen' (sizes), 'Temperaturen' (temperatures), or 'Qualität' (quality). Common adverbs are 'stark' (greatly), 'leicht' (slightly), or 'je nach' (depending on).
Die Qualität der Produkte kann von Hersteller zu Hersteller variieren.
The quality of the products can vary from manufacturer to manufacturer.
To indicate the reason for a variation, the construction 'je nach' (depending on) followed by a noun in the dative is often used.
Die Lieferzeiten variieren je nach Bestimmungsort.
Delivery times vary depending on the destination.
to change
Verändern generally means making something different. Variieren usually means deliberately modifying something within several possible variations while keeping the basic plan or theme. For a general change, verändern is appropriate; when different versions are intended, variieren is the better choice.

Wir variieren den Plan für die verschiedenen Gruppen nur bei den Pausenzeiten.
We are varying the plan for the different groups only in terms of the break times.
Wir verändern den Plan, weil der Veranstaltungsort nicht mehr verfügbar ist.
We are changing the plan because the venue is no longer available.