Pulsus paradoxus is a exaggerated drop in systolic BP, whereas Kussmaul's sign is a rise in JVP.
During inspiration, intrathoracic pressure drops, which causes venous blood to return to the right atrium, and then to the right ventricle. Also, lungs become inflated, pooling the blood inside the lung. Both of these result in decreased venous return to the left ventricle. According to the Frank-Starling mechanism, decreased venous return (=decreased end-diastolic LV volume) would decrease stroke volume, which would be manifested as a decreased systolic BP. If there is another mechanism which further decreases blood return to the left ventricle (such as cardiac tamponade), this physiological response will become exaggerated, using the same flow of events.
As for Kussmaul's sign: Like I've said above, during inspiration, blood will return to the right atrium, meaning JVP would drop. If there is a mechanism through which blood can no longer enter the right heart, it will instead pool backing up, resulting in an increase JVP. Now this part often get mixed up: If there is just cardiac tamponade, there won't be Kussmaul's sign, but there will be elevated JVP. In constrictive pericarditis, elevated JVP and Kussmaul's sign will both be present. Elevated JVP itself does not equal to Kussmaul's sign; Kussmaul's is the rise in JVP with inspiration.
In summary: cardiac tamponade = pulsus paradoxus; constrictive pericarditis = Kussmaul's sign. Both will have elevated JVP.