In a few of my entries on Lang-8.com, several of my Chinese friends have changed 平常 into 通常 and vice versa without providing additional explanation. It it just a matter of personal taste?
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The two words share the same character "常“(common, usual,eternal), so the meanings overlap somewhat. Both of them can mean "commonly, usually", however, they are not exactly the same.
"平常“ means (notice 平 means "plain，commonplace" here）
When something is ordinary, usually you could say it's the most possible case or it's common, that's how the two words have the similar meaning.
sometimes 平常 is used as an adjective,you can say someone is 平常，But you can't say someone is 通常,or you can say some situation is 平常.
Generally, it is the same in speaking, but 通常 is more formal and better use it in a formal contextual.