Actually it's a single case, called Esm alfa3el اسم الفاعل (The Doer) Simply, if you have a 3 letters verb root*, you put the letters instead of the f,3,l in this form (f a 3 e l) I think your differentiation comes mainly from the meaning, because even in English you would say: "The speaker said: I am the sender of the letter". Both speaker and sender being in the same case (some who does the action), differs as the speaker could be (you are speaking, or you already spoke, either ways you are a speaker) and sender means (you have already sent the thing, because we don't normaly say you are sending something, you are a sender). *there is a rule for 4 letters roots as well. Hope I've understood your question well, and explained correctly. Also sorry I changed the translation of the example slightly, because I wasn't sure of your spelling.

sentences were given as an example to explain rules. they were not taken from any text. I just should learn more to understand it

I think it's in Hadith or something, could you write it all so I can get what does it mean and help you ?