For example " 'O yemek yedim.' dedi." means, he sad ' I ate food' . But with söylemek, ''O yemek yediğini söyledi'' means, he sad that he has eaten food. Im not sure if its explanatory but there isnt huge difference.

demek: to say through direct speech | söylemek: to say through indirect speech

in speech, yes i think we can say so. But they can be used in same meaning too, for example 'Sana söylüyorum/diyorum ' means im saying to you. 'Ona ne söyledin/dedin' means what did you say to him/her' or 'Ben birşey demedim/söylemedim' means i sad nothing. So dont classify them too strict.