The item names gold_sword, gold_pickaxe, and gold_axe exist and are usable but gold_shovel does not. You must use golden_shovel. The same applies for wooden tools. wood_<item> exists as item names for sword, pickaxe, and axe but not for shovel.

The item names for sword, pickaxe, and axe can be written using the short form or long form, wood/gold and wooden/golden respectively, but for shovel it can only be written in its long form as wooden or golden.