Is spruse a hardwood

No. It's a softwood.

The difference isn't a matter of wood density. Softwoods come from needle-leaf trees, and hardwoods come from broadleaf trees. The softest wood in the world is balsa, which is extremely soft and lightweight...but because balsa trees are broadleaf, balsa is a hardwood. On the other hand, Radiata pine is roughly as hard as mahogany - which is unquestionably a hardwood - but because it's a needle-leaf tree it is a softwood.