What is the difference between present and current ?Feel free to just provide example sentences.

I'd say that they are basically the same. If you were to say "I am presently in New York," it might sound just a little bit strange to some people who are used to hearing "I am currently in New York." But the two words are generally interchangeable. Though you could say "I am in the present," I do not recommend you say "I am in the current." You could say "I am in the current day" or "I am in the present day." They can almost always be used in the same circumstance, though. Ultimately, it just matters how the two sound in the sentence.