geläufig
common / familiar
Generally known, familiar, or widespread.
Sein Name ist mir geläufig, aber ich kann kein Gesicht zuordnen.
His name is familiar to me, but I can't put a face to it.

common / fluent
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common / familiar
Generally known, familiar, or widespread.
Sein Name ist mir geläufig, aber ich kann kein Gesicht zuordnen.
His name is familiar to me, but I can't put a face to it.

The adjective 'geläufig' (common/fluent) is related to the verb 'laufen' (to run). It describes something that 'runs' well, meaning is fluent, or that is figuratively in circulation and therefore known to many people.
Diese Redewendung ist heute nicht mehr so geläufig.
This idiom is no longer so common today.
When it is about knowledge (a name, a term), 'geläufig' (common/familiar) usually means 'bekannt' (known). When it is about a skill (a language, an instrument), it means 'fließend' (fluent).
Die Abkürzung „z.B.“ ist jedem Deutschlerner geläufig.
The abbreviation 'z.B.' is familiar to every German learner.
In the meaning 'bekannt' (known/familiar), 'geläufig' is almost always used with a person in the dative. The structure is: Something is [mir, dir, ihm, ihr...] geläufig.
Der Name der Autorin ist mir zwar geläufig, aber ich habe noch kein Buch von ihr gelesen.
The author's name is familiar to me, but I haven't read any of her books yet.
In the meaning 'fließend' (fluent), 'geläufig' can also be used as an adverb to describe how well someone performs a skill. It then stands directly with the verb.
Er kann das Musikstück schon sehr geläufig spielen.
He can already play the piece of music very fluently.
sure / safe
'sicher' and 'geläufig' can both describe that someone can do something well and without major mistakes. 'sicher' emphasizes that you act reliably and show no uncertainty. This fits many activities, for example driving, calculating, or speaking. 'geläufig' is more likely to fit language, words, or practiced routines, and means that something goes smoothly and easily. If someone speaks a language well, both can fit: 'sicher' sounds more like control, while 'geläufig' sounds more like fluent use.

Die wichtigsten Formen sind ihm vor der Prüfung schon geläufig.
He is already familiar with the most important forms before the exam.
Nach einigen Fahrstunden fährt Lena schon sehr sicher durch die Stadt.
After a few driving lessons, Lena already drives through the city very confidently.