These phrases are both used for emphasis.
“Needless to say, ______” is another way to state, “It is obvious that _____.”
“That is to say, ______,” is a way to reiterate something. It is the same as “In other words, ______.”
Examples:
“Needless to say, if you are vaccinated, you are less likely to become ill.”
“I love cats. That is to say, cats are wonderful animals.”