der Karren
cart
A simple vehicle, usually with two wheels, pulled by hand or by an animal to transport loads.
Der Gärtner transportierte die Erde mit einem Karren.
The gardener transported the soil with a cart.

cart / old banger
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cart
A simple vehicle, usually with two wheels, pulled by hand or by an animal to transport loads.
Der Gärtner transportierte die Erde mit einem Karren.
The gardener transported the soil with a cart.

You can recognize the colloquial meaning 'altes Auto' (old car) from context. It is often used with derogatory adjectives like 'alt' (old) or 'rostig' (rusty). The original meaning refers to simple carts that you find, for example, in gardening or agriculture.
Er muss seinen alten Karren endlich verkaufen.
He really needs to finally sell his old banger.
The term 'Karren' for a car is colloquial and usually meant negatively or derogatorily. It describes an old, noisy, or unreliable vehicle.
Mit diesem rostigen Karren will ich nicht in den Urlaub fahren.
I don't want to go on vacation in this rusty old banger.
The idiom 'den Karren aus dem Dreck ziehen' (to pull the cart out of the dirt / to pull things out of the mire) is fixed. The person who solves the problem is the subject of the sentence, while 'den Karren' is the accusative object.
Das Team war in einer Krise, aber die neue Managerin hat den Karren aus dem Dreck gezogen.
The team was in crisis, but the new manager pulled things out of the mire.
In its literal meaning, 'der Karren' (the cart) is often used with verbs such as 'ziehen' (to pull), 'schieben' (to push), or 'beladen' (to load), which describe transporting loads.
Zwei Pferde zogen den schweren Karren den Berg hinauf.
Two horses pulled the heavy cart up the mountain.
car / cart
'der Karren' and 'die Karre' can both mean a simple vehicle for carrying loads. In this sense, 'Karren' is often the more neutral form, for example a small cart for pulling. 'Karre' is heard especially in compounds like 'Schubkarre' (wheelbarrow) or 'Handkarre' (handcart). Both words can also colloquially mean an old or bad car. In that case, 'Karre' sounds very typical and often derogatory; 'Karren' is also possible, but less neutral. They can be confused because they look almost the same. The article and the context are important: 'der Karren' is more likely to fit a simple cart, while 'die Karre' very often refers to a bad car or to a wheelbarrow.

Der Bauer zog den schweren Karren über den Hof.
The farmer pulled the heavy cart across the yard.
Nach der langen Fahrt sprang die alte Karre vor dem Haus nicht mehr an.
After the long drive, the old car would not start outside the house anymore.