I believe that the phrase "boys will be boys" was the earliest of these to be created, and the others are imitations of or references to this phrase.
The phrase "boys will be boys" is an idiom meaning "boys will act in ways typical of boys". The most common usage is that someone complains about some undesirable behavior on the part of one or more boys, and some other person responds "Oh well, boys will be boys" meaning that the behavior is of a sort to be expected from boys (perhaps particularly from boys of the relevant age), and that it should not be taken too seriously.
Lexico says that this phrase is: "used to express the view that mischievous or childish behavior is typical of boys or young men and should not cause surprise when it occurs."
Merriam-Webster says the phrase is:
used to indicate that it is not surprising or unusual when men or boys behave in energetic, rough, or improper ways You shouldn't be too hard on them for staying out so late. Boys will be boys
If you say boys will be boys, for example when a group of men are behaving noisily or aggressively, you are suggesting in a light-hearted way that this is typical male behaviour and will never change.
said to emphasize that people should not be surprised when boys or men act in a rough or noisy way because this is part of the male character.
An article drom dictionary.com "Why We Say 'Boys Will Be Boys' But Not 'Girls Will Be Girls'” reads:
Boys will be boys. It’s an idiom we hear tossed around far too often. But, what does it actually mean, and why did we ever start saying it? And … what about girls—who or what will they be?
Who decided boys will be boys, anyway?
The phrase boys will be boys was first recorded in English in 1589. It originated from a Latin proverb: “Children (boys) are children (boys) and do childish things.” While a bit obvious, if it had remained intact as such, it wouldn’t be so problematic. Children in fact do childish things, and that’s to be expected to some degree.
Like a bad game of telephone, however, the phrase has morphed over the years into a flippant way to excuse the actions and attitudes of boys and men of all ages. It’s typically used to explain rowdy or naughty behavior—things like jumping in mud puddles, roughhousing, and raising Cain. It’s also, unfortunately, used to explain away things like sexual assault allegations and other serious crimes. It doesn’t hold individuals responsible for their behavior and choices but rather infers all males are preprogrammed to act in such ways.
Beyond that (which was a huge “that”), the phrase promotes gender stereotypes. Not all boys like to get dirty, some prefer roses to roughhousing and, thankfully, most men aren’t violent. Like the phrase, boys don’t cry, it sets a standard for what male behavior should be. Instead of assuming men are individuals with unique personalities, it promotes that idea that anyone who doesn’t live up to this arbitrary definition of masculinity is abnormal. It attempts to put a neat and tidy bow of oversimplification on individual behavior, and it’s time we stop saying it … and more importantly, stop believing it.
I find no dictionary entries for the phrase "men will be men", although there are many articles, positive, and negative, about the phrase. Typically it is used to express (or to ridicule) the idea that certain kinds of poor, even criminal, behavior are typical of men, and that this i only to be specter and will never change.