Arabic, Arabian would refer to the geographic region of the Arabian peninsula. The dialects are on a spectrum, neighboring countries might understand each other reasonably well, but not countries further apart. Syrian, Lebanese and Palestinian share a lot of features, same goes for gulf countries, Egyptian is pretty distinct but well known outside the country due to its output of movies, music and tv series, Algerian and Tunisian are pretty similar, Moroccan’s kind of its own thing, Maghrebi dialects also include a lot of vocabulary from Berber languages, which won’t be understood in other regions. Finally, in most countries, local dialects are not taught in school but rather Fusha, or modern standard Arabic, which is the language you’ll hear on the news or read in the papers, and is common to the entire Arabic-speaking world. People don’t speak it day to day but usually understand it well and can communicate in a mix of that and their dialects if they’re speaking to someone from another Arabic-speaking country.