The difference is very subtle between word "تكلم" and word "تحدث" (speaking and talking ) in Arabic, that speech may be without the presence of a second party who hears the speech, and in this cases we use "تكلم", but talking is with the presence of a second party, here we use "تحدث". But they usually use them without distinguishing between these meanings.

يتحدّث talk (present) تحدّث talked(past verb) حَدِيث talk (verbal noun) يتكلّم speak تكلّم spoke كلام speech

"Atahadatho*" comes from "hadath" which means: event; so the original meaning is "to talk about something that happened to you". While "atakalamo*" means just talking, whether about yourself or anything else. But, as others said before me, both words are used interchangeably nowadays.

actually no difference, we use them interchangeably. In some cases we prefer using one over the other, but you can use them as you like . But I will tell you something You say speak and say talk.... The same

There's actually no difference, we use them interchangeably. In some cases we prefer using one over the other, but still, using either of them in whatever context would sound just normal and correct.