This is interesting. I'm trying to learn Spanish and I can see this is going to be a problem for me! In Spanish, I have just learned that there are three separate names, "punto seguido," "punto aparte," y "punto final." In English, there is no such distinction. A full stop, or "period" as we say in the United States, is just a period.
I've never had to give or take dictation so I don't know exactly how one would indicate new paragraphs aloud. I think you'd just say "New paragraph." This isn't something that is taught in English classes--not to me, anyway.