In the US the primary list is the Specially Designated Nationals list maintained by ofac, supplemented by sectoral and country-based programs. The UK, EU and UN maintain their own, and firms typically screen against several.
Liability is strict. There is no intent requirement, and penalties apply even where a payment was processed by mistake through fuzzy name matching failure. That is why screening produces heavy false positive volumes and manual review queues.
Consequences for a matched transaction differ: blocking freezes funds in a segregated account, while rejection returns them. Both are reportable, and the customer generally cannot have the money back without a licence.
Related: ofac, politically-exposed-person, travel-rule, enhanced-due-diligence, anti-money-laundering