Why is the solubility of sodium acetate trihydrate so much lower than anhydrous sodium acetate?
The values of solubility for these salts are $100\%$ correct. Your understanding of solubility is also correct. What you didn't know (probably) is that solutions can exist in a non-equilibrium state. In case of anhydrous sodium acetate, it dissolves in water forming so-called supersaturated solution, which is metastable. Eventually, crystals of sodium acetate trihydrate will precipitate out of the solution, forming a system which is in the thermodynamic equilibrium.