
überholen
to overtake
To drive or walk past another vehicle or person moving in the same direction.
Auf dieser schmalen Straße ist es zu gefährlich, den Traktor zu überholen.
On this narrow road, it is too dangerous to overtake the tractor.
to overtake / overhaul
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to overtake
To drive or walk past another vehicle or person moving in the same direction.
Auf dieser schmalen Straße ist es zu gefährlich, den Traktor zu überholen.
On this narrow road, it is too dangerous to overtake the tractor.

to overtake
To become better, more modern, or more successful than someone or something else.
Technologisch hat Südkorea Japan in vielen Bereichen überholt.
Technologically, South Korea has overtaken Japan in many areas.

to overhaul
To thoroughly inspect, service, and repair something, especially a machine or device, in order to bring it back into good condition.
Der Motor des Oldtimers muss dringend überholt werden.
The engine of the vintage car urgently needs to be overhauled.

to pull something on
(Separable) To quickly put on an item of clothing. This meaning is rare and rather outdated.
Er holte sich nur schnell eine Jacke über und verließ das Haus.
He just quickly pulled on a jacket and left the house.
'Überholen' is an inseparable verb in most meanings (to overtake, to become better, to service). Only in the rare, outdated meaning 'sich etwas anziehen' (to put something on) is it separable.
Er hat den LKW überholt.
He overtook the truck.
Since the verb is usually inseparable, the past participle is formed without 'ge-'. So it is 'hat überholt' (has overtaken/overhauled), not 'hat übergeholt'.
Die Firma hat ihre Konkurrenten technologisch überholt.
The company has technologically overtaken its competitors.
The context makes the meaning clear: If it is about vehicles, 'vorbeifahren' (to drive past/overtake) is meant. If it is about competition or performance, it means 'besser werden' (to become better). If it is about machines or devices, 'warten/reparieren' (to service/repair) is meant.
Der Radfahrer überholt das Auto im Stau.
The cyclist overtakes the car in the traffic jam.
In this meaning, the verb is often used with an accusative object that indicates who or what is being overtaken. Giving the direction is also common.
Man darf hier nicht rechts überholen.
You are not allowed to overtake on the right here.
When it means 'warten/reparieren' (to service/repair), the objects are typically technical devices or vehicles, for example 'den Motor überholen' (to overhaul the engine), 'die Bremsen überholen' (to overhaul the brakes), or 'die Software überholen' (to overhaul/update the software).
Die Werkstatt hat den Motor komplett überholt.
The repair shop completely overhauled the engine.
to wait / maintain
To warten a machine means to check it regularly and keep it functioning. To overhaul it is more comprehensive: the machine is thoroughly inspected and repaired as needed so that it returns to good condition. Use „warten“ for routine work and „überholen“ for a fundamental repair.

Die Werkstatt überholt die alte Maschine gründlich und ersetzt ihre beschädigten Teile.
The workshop thoroughly overhauls the old machine and replaces its damaged parts.
Die Werkstatt wartet die Maschine jedes Jahr und prüft ihre wichtigsten Teile.
The workshop services the machine every year and checks its most important parts.