"Afterwards" is a very frequently used word. It's ordinary everyday English, written and spoken. It's an adverb. It just means "at a later time." It's basic vocabulary. And it just means "later," it doesn't imply "caused by." Example: "We went to the movies, then afterwards we had coffee." "Aftermath" is not commonly used. It's not basic vocabulary. It's a noun. It refers to the results, usually bad or chaotic results, caused by an event, usually a big event. If I hear "In the aftermath of..." the next words I expect to hear are "...the war." Some examples from Google News: "In the aftermath of this tragic event, Justice Department officials have been in touch with Mr. Garner's family members." "The rush to place blame in the aftermath of MH17 has been a credit to no one." "In the aftermath of the Industrial Revolution, functionality was paramount for businesses to win their clients' dollars."

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