What is the difference between と話す and に話す


Just as the title says, I'd like to know the difference between 先生に話す and
先生と話す, since they are both correct (if I'm wrong please correct me)




私は先生と話す means "I and the teacher have a conversation", so they talk to each
other".

私は先生に話す means "I tell something to the teacher", so only I speak and the
teacher listens to it.




私は先生と話す means "I and the teacher have a conversation", so they talk to each
other".

私は先生に話す means "I tell something to the teacher", so only I speak and the
teacher listens to it.

