Before 1582 the rule is just simpler. If it is divisible by 4 it's a leap year. So the difference is relevant for years 300, 500, 600, 700, 900 etc. For ranges spanning those years the Gregorian algorithm would result in results not matching reality.
When the Julian calendar was really adopted I don't know. Certainly not 0001-01-01. And of course it varies by country like Gregorian.
From Wikipedia:
>The Julian calendar was proposed in 46 BC by (and takes its name from) Julius Caesar, as a reform of the earlier Roman calendar, which was largely a lunisolar one.[2] It took effect on 1 January 45 BC, by his edict.
Not knowing the year seems unhinged somehow.
It was already known to scholars that the length of a (tropical) year is close to 365-and-a-quarter days since at least 238 BC (when Ptolemy III tried to fix the length of the year in the Egyptian calender to 365-and-a-quarter days in the Canopus Decree).
However, due to a mistranslation the Roman pontifices got it wrong at the introduction of the Julian calendar. The Romans counted inclusively, which means: counting with both the start and end included. (That is why Christians say in a literal translation from Latin that Jesus has risen on the third day, even though he died on a Friday and is said to have risen two days later, on the next Sunday.)
In the first years of the Julian calendar, the Roman pontifices inserted a leap day “every fourth year”, which in their way of counting means: every 3 years. Authors differ on exactly which years were leap years. The error got corrected under Augustus by skipping a few leap years and then following the “every 4 years” rule since either AD 4 or AD 8. See the explanation and the table in https://en.wikipedia.org/wiki/Julian_calendar#Leap_year_erro...
Also note that at the time, years were mostly identified by the names of the consuls rather than by a number. Historians might use numbers, counting from when they thought Rome was founded (Ab urbe condita), but of course they differed among each other on when that was. The chronology by Atticus and Varro, which placed the founding of the city on 21 April 753 BC in the proleptic Julian calendar, was not the only one.