The chemical formula of backing powder is sodium hydrogen carbonate (NaHCO3); whereas, that of washing soda is sodium carbonate (Na2CO3. 10H2O).
Sodium hydrogen carbonate on heating gives CO2 gas which will turn lime water milky whereas no such gas is obtained from sodium carbonate.
2NaHCO3 {\overset{heat}{\longrightarrow}} Na2CO3 + H2O + CO2
Na2CO3.10H2O {\overset{heat}{\longrightarrow}} Na2CO3 + 10H2O