der Ausrutscher
slip
A sudden slide on a slippery surface, often leading to a fall or near fall.
Ein kleiner Ausrutscher auf dem vereisten Gehweg führte zu einem gebrochenen Arm.
A small slip on the icy sidewalk led to a broken arm.

slip / lapse
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slip
A sudden slide on a slippery surface, often leading to a fall or near fall.
Ein kleiner Ausrutscher auf dem vereisten Gehweg führte zu einem gebrochenen Arm.
A small slip on the icy sidewalk led to a broken arm.

'Der Ausrutscher' (the slip/lapse) is the noun form of the separable verb 'ausrutschen' (to slip). It describes the event or action of the verb, that is, the sudden sliding.
Pass auf, dass du auf dem nassen Boden nicht ausrutschst.
Be careful not to slip on the wet floor.
The literal meaning refers to a slippery surface such as ice or a wet floor. You can recognize the figurative meaning from words that relate to behavior or speech, such as 'Bemerkung' (remark), 'Fehler' (mistake), or 'peinlich' (embarrassing).
Sein Ausrutscher auf der Bananenschale sah lustig aus.
His slip on the banana peel looked funny.
In the literal meaning, the preposition 'auf' with the dative is often used to name the surface on which someone slips.
Ein Ausrutscher auf der Treppe kann gefährlich sein.
A slip on the stairs can be dangerous.
In the figurative meaning, 'Ausrutscher' (lapse) is often combined with adjectives like 'peinlich' (embarrassing), 'verbal' (verbal), or 'einmalig' (one-time) to describe a social or linguistic mistake.
Der Politiker bezeichnete seine Aussage später als einmaligen Ausrutscher.
The politician later described his statement as a one-time lapse.
mistake / error
'der Fehler' and 'der Ausrutscher' can both mean a wrong action or statement. 'Fehler' is the general word and can be one-time, repeated, small, or serious. In this relation, 'Ausrutscher' more often means a small, one-time mistake or a thoughtless remark. It is often also used to say that this behavior is not typical for the person. The words can be confused because an Ausrutscher is a kind of Fehler. But 'Ausrutscher' sounds milder and more personal. For a factual or serious mistake, 'Fehler' is usually more precise.

Simons unfreundlicher Kommentar war nur ein Ausrutscher, denn sonst ist er sehr höflich.
Simon’s unfriendly comment was just a lapse, because he is usually very polite.
Der Gast findet einen Fehler auf der Rechnung und spricht den Kellner darauf an.
The guest finds a mistake on the bill and asks the waiter about it.