No - the ingredient list on the bar is considerably abbreviated compared to the stick. Also there are quite a number of differences.
Palmolive stick: Potassium Hydrogenated Tallowate, Sodium Tallowate, Sodium Cocoate, Aqua, Glycerin, Parfum, Olea Europaea, Elaeis Guineensis, Tetrasodium EDTA, Tetrasodium Etidronate, BHT, Buytlphenyl Methypropional, Citronellol, Coumarin, Hydroxyisohexyl 3-cyclohexene carboxaldehyde, Limonene, Linalool, CI11680, CI12490, CI74260, CI77891