A new definition for the symmetries of Ito and Stratonovich dynamical system is given. Determining systems of symmetries for Ito and Stratonovich systems have been obtained, and their relation has been discussed. It has been shown that some of the Lie point symmetries of the Fokker - Planck equation can be constructed using the symmetries of Ito dynamical systems. Conserved quantities can be found from the symmetries of stochastic dynamical systems which do not arise from a Hamiltonian. The results have been applied to an example.