What is the chance that a roll of two 6-sided dice will turn up 3, as a total? The chance is 1 in 18. Why? Because (1, 2) and (2, 1) are two possible outcomes. More precisely, reality distinguishes between the dice.

Outcome 1: Dice 1 is 1 and dice 2 is 2
Outcome 2: Dice 1 is 2 and dice 2 is 1.

Even more precisely, if you roll the dice thousands of times, outcome 1 happens once every 36 times, and outcome 2 happens once every 36 times.

Note that 1 in 18 amounts to a statistical frequency of 5.56% that you will roll a 3.

But:
What if you rolled the dice thousands of times and the frequency was instead 1 in 36? ... which is 2.78%

Assume that they are perfectly balanced and "ideal" dice. If we assume that outcomes 1 and 2 are the same outcome, we can predict the 2.78%. But what does this mean? How can both outcomes not be two possible things that happen when you roll the dice?

Because this is what happens with tiny "quantum" particles like electrons, photons and protons. We can predict their aggregate statistical observed behavior by assuming not that they are all only identical but that all electrons (for example) are also "indistinguishable" from each other.

What is the difference? What is the difference between being identical and being indistinguishable? As far as I know, saying that they are indistinguishable only means that the particles behave as if outcomes 1 and 2 are the same thing.

Summary: Currently, in Quantum Physics, the hidden secret is that you can't say that electrons follow quantum statistics "because" they are indistinguishable. They are called indistinguishable because they obey quantum statistics. Why they are indistinguishable is still a true mystery in Physics, a mystery that Science has hidden for almost a century.

Hidden behind the veneer that in the Quantum Realm, reality is supposed to be "fuzzy" and not objective.