I can speak. I can speak to her. I speak about something. I can tell my dog to speak, but I cannot tell him to talk. Speak is more formal, but is also closer to 'make sounds'.
Talk is closer to 'say words'.
I can talk. I can talk to someone. With months, Japanese students become confused because it is difficult to say 'th' like in 'tooth' and 's' as in 'dress' together. Often I hear 'tthhhsssss' which is too strong. More often I hear 'mons ez' which is not right.