schleppen
to lug
To pull or carry something heavy with effort.
Er musste die schweren Koffer die Treppe hoch schleppen.
He had to lug the heavy suitcases up the stairs.

to lug / to drag
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to lug
To pull or carry something heavy with effort.
Er musste die schweren Koffer die Treppe hoch schleppen.
He had to lug the heavy suitcases up the stairs.

The verb 'schleppen' can be used reflexively or non-reflexively. When a person or thing moves a heavy object, use 'schleppen' with the accusative. When a person or a process moves with difficulty, use 'sich schleppen'.
Ich habe den ganzen Tag schwere Kisten geschleppt.
I lugged heavy boxes around all day.
When you use 'schleppen' instead of 'tragen' (to carry), you emphasize the great effort, the heavy weight, or the reluctance involved in the activity. It sounds more strenuous and often a little negative.
Musst du wirklich all diese alten Zeitschriften in die neue Wohnung schleppen?
Do you really have to lug all these old magazines to the new apartment?
In this meaning, 'schleppen' is used almost exclusively for pulling vehicles or ships. In this context, the verb 'abschleppen' (to tow away) is also often used.
Ein Traktor schleppte das im Schlamm steckende Auto heraus.
A tractor towed the car that was stuck in the mud out.
The reflexive form 'sich schleppen' is often used figuratively for processes that make progress only very slowly and with difficulty. It is frequently used together with the adverb 'dahin'.
Die Besprechung schleppte sich ohne Ergebnis über drei Stunden dahin.
The meeting dragged on for three hours without any result.
to pull / move
'ziehen' and 'schleppen' can both mean that you move something using force. 'ziehen' is neutral: you move something toward yourself or along behind you. 'schleppen' emphasizes that something is heavy and that moving it takes effort; sometimes you also carry it while doing so. With vehicles, 'schleppen' can also mean that another vehicle tows it. Learners may confuse the words because both involve using force. If only the direction is important, 'ziehen' usually fits. If the load is heavy or the action is strenuous, 'schleppen' fits better.

Vor der Reise schleppt die Familie zwei schwere Koffer zum Bahnhof.
Before the trip, the family lugs two heavy suitcases to the train station.
Tom zieht den Stuhl näher an den Tisch.
Tom pulls the chair closer to the table.