What is the difference between indistinguishable particles and identical particles?
If I create an electron on earth and someone else creates an electron on Andromeda, they're identical particles. They have the same quantum numbers, they're both excitations of the electron field. However they're distinguishable by means of their spatial separation. Their wavefunctions don't overlap.
Edit: perhaps I should add that not everyone uses the two words in this strict sense. Sometimes they're used interchangeably, but blurring them carries with it the danger of taking seriously the entanglement implied by antisymmetrizing across all existing electrons.
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Two particles are the same if you can't tell the difference, that is if the exchanging operator commutes with all observables. In this QM context thus indistinguishable and identical particles mean the same thing.