Dot: this mark can be used for different contexts, for example, a mark used in orthography, as above an i.
Period: this one is just about grammar and is used at the end of a sentence or paragraph .
the first one is just a mark, the second one is a grammatical mark.
Hope I clarified your doubt, if you need more ESL grammar lessons I will be more than happy to help you, have a nice day! :)