Learn Russian: Это разные вещи. - These are different things.

When это is used as a standalone subject to introduce or point something out ("This is..." or "These are..."), it does not change form. It stays это even if the noun following it is plural, like вещи (things). You only use the plural эти when it acts as an adjective attached directly to a noun (for example, эти вещи means "these things").

Where is the verb for "are" in this sentence?

In Russian, the present tense forms of the verb "to be" (am, is, are) are almost always left out. The sentence literally reads "These [are] different things."

The singular word for "thing" is вещь. Why does the plural вещи end in -и?

Вещь is a feminine noun ending in a soft sign (-ь). To make these nouns plural, you replace the soft sign with -и. Additionally, a major Russian spelling rule states that you can never write the letter ы after щ—you must always use и.

Why does the adjective разные (different) end in -ые?

-ые is the standard ending for plural adjectives in the nominative case. Because the noun it describes, вещи (things), is plural, the adjective must also take this plural form to match.