TITLE: In plain language, what's the difference between two things that are 'equivalent', 'equal', and 'identical'?
QUESTION [49 upvotes]: In plain language, what's the difference between two things that are 'equivalent', 'equal', 'identical', and isomorphic?
If the answer depends on the area of mathematics, then please take the question in the context of logical systems and statements.

REPLY [6 votes]: Given you have a person "John Doe", then to...

his picture he is 'isomorphic'
his brother he is 'equivalent'
his twin brother he is 'equal'
himself he is 'identical'