For example: Julius Caesar was assassinated on the 15th of March, 44 BC. Is this a date in the Gregorian or Julian calendar?
It must be really confusing with all these different systems. When one source for a date concerning an event is in the Jewish calendar, another in the Arabic calendar and another in the Gregorian.
Or is this generally not so important?
Usually historians can convert dates from entirely different calendrical systems into their Gregorian equivalents as needed; for example historians writing on Islamic history will often list dates in both the Islamic calendar and their Gregorian conversion and Mesoamericanists can use an established correlation(most notably the GMT correlation used for Mayan long count dates) to convert Long Count or Calendar Round dates into their Gregorian equivalents.
Typically, there is BCE, which is Before Common Era, and CE, Common Era, which is equivalent to the Christian BC and AD, introduced by the 6th-century Christian monk Dionysius Exiguus.
Most other calenders, such as the Chinese or Islamic calenders, are easily converted into BCE/CE.