At their base definitions, they're the same thing： 说 means "speak" and 说话 means "speak dialogue," but obviously, when you're speaking, you're already speaking dialogue.
However, like so many terms in Chinese, they're used differently in different situations. 说 is used when referring to speaking specifically about something, whereas 说话 is used when referring to speaking in general. Here's an example:
”你明明知道！她在哪里？快说！“ This means "You clearly know! Where is she? Speak up!" In this situation, the speaker wants the listener to tell him/her something specific (where the woman he/she is looking for is), so 说 is used.
"他已经三岁了，为什么还不会说话？“ This means "He's already three-years-old; why doesn't he know how to speak yet?" In this situation, the speaker is wondering not about something specific that the boy is saying, but about why the boy cannot speak in general yet despite his age.
I hope this helps. Please let me know if you have any further questions.