urethane foam
Refers specifically to the foam material, commonly used in cushions, mattresses, and insulation.
from German Urethan
This cushion is made of urethane foam.
polyurethane
Broader term for the polymer itself, used in coatings, adhesives, and various industrial applications.
Polyurethane paint is highly durable.
Loanword from German 'Urethan'.