When you’re talking about wage prices, definition 1 is the relevant definition. Definition 1 includes both supply and demand. You have a worker willing to work

When you’re talking about wage prices, definition 1 is the relevant definition. Definition 1 includes both supply and demand. You have a worker willing to work for $50/hr and someone willing to pay them $50/hr. Definition 2 is only taking into account demand. You have a supplier who has set their price, but no buyers at that level.