Russian is written in a script known as Cyrillic. Some Cyrillic letters correspond exactly to Roman letters, e.g. A = A. But some require transliteration, and transliteration techniques can change over time. So in this case, "tsar" is "царь." "aр" is uncontroversially just "ar" — no difference, really, just a substitution. ("ь" is a silent letter that tells you how [the consonant is pronounced](https://en.wikipedia.org/wiki/Palatalization_(phonetics)) — if one is being picky, one transliterates it with an apostrophe or prime symbol.) But ц is a letter we don't have in Roman scripts, and sounds like a "t" that slides into an "s" sound (similar to the "zz" sound in "pizza"). So Tsar, Tzar, Czar, Csar — those are all just attempts to render a letter we don't really have into a Roman script. What can get extra complicated is that transliteration is also based on how things sound and how sounds are expressed in your language, and that can change even between languages with the same script. So just for example, the Germans transliterate the above as "Zar" because their "Z" sound fits the bill better than the English "Z" sound, or the English "Ts" sound.

All of this can be rather confusing since letters (in all languages) change their pronunciations radically depending on their place in the word. So the "в" letter in Cyrillic is transliterated as a "v", but if it comes at the end of a word with a vowel it usually sounds like an "ff" sound. Молотов = Molotov, but is pronounced more like "Molotoff" in Russian.

Some organizations (e.g. journalists) have stylesheets with standardized transliterations of some words (e.g. sticking to "czar" for consistency, when usually "tsar" would be more common for a "fresh" transliteration of a word today), and of course there are governmental regulations and academic norms for preferring certain types of transliterations for consistency. As you can see from Google Ngrams, "tsar" surpassed "czar" around the time of the Russian revolution, but there is still a lot of usage of the term "czar." (Czarina/tsarina is an interesting graph.)

There are probably some interesting clusters behind who uses which and when. Academic historians are almost always going to use "tsar" to talk about the Russian rulers — it has been the standard for a long time. But journalists are much more likely to use "czar" when using it metaphorically, e.g. the "[drug czar](https://en.wikipedia.org/wiki/Czar_(political_term))." There are standard ways that academics (at least in the United States) tend to transliterate things these days, though exceptions are often made for proper names that are already well-known under older transliterations. So it can tell you something about the person or organization who uses a given transliteration.

Russian царь and German Kaiser have the same etymological root — Caesar in Latin. The Russian language itself has many linkages with other languages, but that is separate from their script and transliteration issues.