What is the difference between 'identical' and 'indistinguishable'?

Here are some identical things:
• Fundamental particles of the same type (eg 2 electrons).
• Perfectly replicated DNA molecules
• A digital image (before it is printed or displayed on a screen)
• A poem  remembered accurately by 2 people.
• Two identical numbers

Here are some indistinguishable things (or are they?):
• Copies of the same book - or any mass-produced product.
• 'Identical' twins
• Peas in the same pod