die Haftung
liability
The legal obligation to be responsible for damage that has occurred or for debts, and to provide financial compensation; responsibility.
Eltern haften für ihre Kinder.
Parents are liable for their children.

liability / traction
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liability
The legal obligation to be responsible for damage that has occurred or for debts, and to provide financial compensation; responsibility.
Eltern haften für ihre Kinder.
Parents are liable for their children.

'Haftung' comes from the verb 'haften'. This verb has two meanings that are reflected in the noun: 'für etwas haften' (to be liable for something) leads to legal liability, and 'an etwas haften' (to stick to something, to hold) leads to physical traction or adhesion.
Der Hersteller haftet für Produktfehler.
The manufacturer is liable for product defects.
The context makes the meaning clear. If it is about law, contracts, money, or damage, legal responsibility is meant. If it is about tires, roads, glue, or surfaces, physical grip is meant.
Die Firma übernimmt die volle Haftung für den Transportschaden.
The company accepts full liability for the transport damage.
In a legal context, typical expressions are 'die Haftung übernehmen' (to accept liability), 'die Haftung ausschließen' (to exclude liability), or 'jemanden in Haftung nehmen' (to hold someone liable).
Bei grober Fahrlässigkeit kann man die Haftung nicht ausschließen.
In cases of gross negligence, liability cannot be excluded.
In a physical context, people often say that something 'gute Haftung hat' (has good traction), 'schlechte Haftung hat' (has poor traction), or 'die Haftung verliert' (loses traction). This is especially common for car tires.
Auf der vereisten Straße verlor das Auto die Haftung.
On the icy road, the car lost traction.
guilt / debt
'die Schuld' and 'die Haftung' can both have to do with responsibility for damage or with money. 'Schuld' is the more general word: someone can be to blame for a mistake, or someone can have debts. 'Haftung' is much more legal in meaning. It means that someone must be legally or contractually responsible for damage and often has to pay money. Learners may confuse the words because both occur after damage has happened. In everyday language, people often say 'Schuld'; in contracts, insurance, and legal matters, 'Haftung' is more common.

Bei Schäden am Mietwagen ist die Haftung im Vertrag genau geregelt.
In the case of damage to the rental car, liability is precisely regulated in the contract.
Mein Vater nahm die Schuld auf sich, obwohl der Fehler im ganzen Team passiert war.
My father took the blame, even though the mistake had been made by the whole team.