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Evoke vs. Invoke
Only because they end in the same four letters ("-voke"), it doesn't mean that "evoke" and "invoke" have identical meanings. Even so, many people are confused by their similarity and consider "evoke" and "invoke" are synonyms. As a result, the situation when "evoke" is used instead of "invoke" and vice-versa is quite frequent.
Yet, the fact that this wrong situation is getting common does not mean that it is also correct. "Evoke" is distinct from "invoke", from their spelling to their pronunciation and meaning.
Evoke vs. Invoke
You should notice that these two English verbs have completely different meanings. Consequently, the context where you can use "evoke" is not appropriate for "invoke" as well, as it will change the message of your phrase. So let's find out what each word means and how to use it correctly in order to avoid misspellings and confusing messages in the future.
 When do we use "evoke"?
 "Evoke" is a verb referring to the action of making someone recall some past events or remember certain situations, feeling certain emotions again. It is a common word in English, but it should only be used in appropriate contexts that refer to the action that causes some memories and feelings to be experienced again.
Example: All that your story is doing is to evoke my own teenage memories. - referring to the action of making someone remember certain memories.
When do we use "invoke"?
"Invoke" is a completely different English verb, more frequently used in a formal language, usually in a legal context. It is defined as the action of using a rule (a law in general) in order to support an action, a decision, a behavior etc.
Example: If you need me to justify my actions, I can invoke a great reason and a great law behind my every decision. - used with the meaning of using a solid argument (law) to support one's behavior.
Conclusion
As you could easily notice from the examples provided above, "evoke" and "invoke" refer to very distinct actions, even though they might look and sound similar in their endings. You should make sure you use them in the right contexts and never confuse them, if you want your message to be correctly understood and interpreted.