How does an “opening sentence” differ from a “topic sentence”?

From LitWiki

The topic — or “opening” — sentence that begins your essay will be a bit different from your body’s topic sentences: it will be less specific, shorter, and more dynamic.

The opening sentence, like the essay’s title, should not be specific, but should catch the reader’s attention with a short, interesting statement that will begin your introduction. Nothing intimidates a reader more than a wall of text, beginning with a long, complex argument. Use the opening sentence to catch your reader’s attention by making it short and interesting:

Life in the twenty-third century is great.

Unlike your paragraphs’ topic sentences, this sentence provides only a hint to pique your reader’s interest. Here, no cumbersome detail is used; only a taste of the essay is needed to inspire the reader’s hunger for more.

Also see What is a “topic sentence”?

Composition FAQ