What’s the difference between “wrinkle” and “crinkle” when they are both verbs?

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They are both verbs.
They can also both be nouns.

The two words are very similar, with almost the same meaning.

Crinkle is also a sound, like the sound of wrinkling and moving aluminum foil, or the sound of broken ice floating on moving water.

Please make up the bed properly. Smooth all of the wrinkles out of the blankets.
When I crinkled up the plastic wrapping it made a noise that woke up the cat.

To wrinkle is to add bumps and folds.
To crinkle is to add bumps, folds, creases and perhaps even breaks in the material, with a crunching and breaking sound.

You can wrinkle a sheet on a bed.
You can crinkle plastic, ice or foil.

They are almost the same, but if it makes a sound it is probably a crinkle.