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I would say that both 变 (biàn) and 易 (yì) have the same (or very similar) meaning, dealing with "something that changes", like in "易经" (the Book of changes) or "变温层" (troposphere).
Is this assumption correct?
What are differences and similarities? In which context one should be used in place of the other?
变 is mainly used as a verb for "change; alter; turn (e.g. turn into a dog)"
易 is mainly used as a verb component in a compound word. Mostly indicates 'transfer' (from one to another). 易 is not used as a verb on its own in day to day speech in modern Chinese
Look at the compound words contain these two characters
变化 - change
转变 - change; transform
易手 - change hand -- transfer ownership
交易 - exchange -- mutually transfer goods or money
