No, Both the steam and boiling water are at the same temperature. (as long as the temperature of the material of which the kettle is made is less than 100 degree, because in case its temperature is >100, the steam may absorb heat from the kettle by conduction)
The reason that steam feels hotter is the latent heat stored in steam. The phase change from water -> steam takes place at constant temperature (100°). However the water absorbs heat energy equal to the latent heat capacity of water/steam to get converted to steam.
Hence although the temperature of water and steam may be same, there is a large difference between the heat energies stored in them.