to wander / digress / roam
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to wander
To let one's gaze or thoughts wander or move around without a fixed goal.
Während der langweiligen Präsentation ließ er seinen Blick aus dem Fenster schweifen.
During the boring presentation, he let his gaze wander out the window.
You can recognize the meaning of 'schweifen' (to wander/digress/roam) from the object: If it refers to 'Blick' (gaze) or 'Gedanken' (thoughts), it is about wandering around. If it refers to 'Thema' (topic), it is about digressing. If it refers to people or animals, it is about roaming around.
Sein Blick schwiff unruhig durch den Raum.
His gaze wandered restlessly around the room.
In this meaning, 'schweifen' (to wander) is very often used in the fixed construction with the verb 'lassen' (to let): 'den Blick schweifen lassen' (to let one's gaze wander) or 'die Gedanken schweifen lassen' (to let one's thoughts wander).
Am Strand ließ sie ihre Gedanken in die Ferne schweifen.
On the beach, she let her thoughts wander into the distance.
When it is about getting away from a topic, the separable verb 'abschweifen' (to digress) is almost always used today. It is more common and clearer than the simple 'schweifen' (to digress).
Entschuldigung, ich bin vom Thema abgeschweift.
Sorry, I digressed from the topic.
The meaning 'umherziehen' (to roam around) is archaic and today is used almost only in literary or historical texts.
In alten Gedichten liest man von Rittern, die durch die Wälder schweiften.
In old poems, you read about knights who roamed through the forests.
When 'schweifen' (to roam) describes movement from one place to another, the perfect tense is formed with the auxiliary verb 'sein' (to be).
Die Wölfe sind nächtelang durch das Revier geschwiffen.
The wolves roamed through the territory for nights on end.
to hike / migrate / wander
'wandern' and 'schweifen' can both describe movement without a very fixed point. 'wandern' is normally used for people who walk longer distances in nature. It can also mean figuratively that something slowly changes location. 'schweifen' is used today mainly for one's gaze or thoughts: they move without a clear goal. As physical movement, 'schweifen' sounds rather literary or old-fashioned. The words can be confusing because you can also say that thoughts 'wandern' (wander). But the more natural pattern is: people 'wandern' in the forest; thoughts or gazes 'schweifen ab' or 'schweifen umher' (wander off or wander around).
Während des langen Vortrags schweifen seine Gedanken immer wieder ab.
During the long lecture, his thoughts keep wandering off.
Am Sonntag wandern wir drei Stunden durch den Wald.
On Sunday, we are hiking through the forest for three hours.