Justice Gorsuch wrote for the majority and his opinion provides a clear explanation of the categorical approach. If you practice in federal court, you should read it.
"To determine whether a federal felony may serve as a predicate for a conviction and sentence under the elements clause [] we must apply a 'categorical approach.' We must because the clause poses the question whether the federal felony at issue 'has as an element the use, attempted use, or threatened use of physical force.' And answering that question does not require—in fact, it precludes—an inquiry into how any particular defendant may commit the crime. The only relevant question is whether the federal felony at issue always requires the government to prove—beyond a reasonable doubt, as an element of its case—the use, attempted use, or threatened use of force."
"Whatever one might say about completed Hobbs Act robbery, attempted Hobbs Act robbery does not satisfy the elements clause. Yes, to secure a conviction the government must show an intention to take property by force or threat, along with a substantial step toward achieving that object. But an intention is just that, no more. And whatever a substantial step requires, it does not require the government to prove that the defendant used, attempted to use, or even threatened to use force against another person or his property."
Importantly, the Court also rejected the government's attempt to "fault[] Mr. Taylor for failing to identify a single case in which it has prosecuted someone for attempted Hobbs Act robbery without proving a communicated threat." The Court stated: "what does that prove? Put aside the fact that Mr. Taylor has identified cases in which the government has apparently convicted individuals for attempted Hobbs Act robbery without proving a communicated threat. Put aside the oddity of placing a burden on the defendant to present empirical evidence about the government’s own prosecutorial habits. Put aside, too, the practical challenges such a burden would present in a world where most cases end in plea agreements, and not all of those cases make their way into easily accessible commercial databases. An even more fundamental and by now familiar problem lurks here. The government’s theory cannot be squared with the statute’s terms. To determine whether a federal felony qualifies as a crime of violence, § 924(c)(3)(A) doesn’t ask whether the crime is sometimes or even usually associated with communicated threats of force (or, for that matter, with the actual or attempted use of force). It asks whether the government must prove, as an element of its case, the use, attempted use, or threatened use of force."
The Court also distinguished Duenas-Alvarez and its “realistic probability” test. "First, the immigration statute at issue in Duenas-Alvarez required a federal court to make a judgment about the meaning of a state statute. Appreciating the respect due state courts as the final arbiters of state law in our federal system, this Court reasoned that it made sense to consult how a state court would interpret its own State’s laws. Meanwhile, no such federalism concern is in play here. The statute before us asks only whether the elements of one federal law align with those prescribed in another. Second, in Duenas-Alvarez the elements of the relevant state and federal offenses clearly overlapped and the only question the Court faced was whether state courts also 'appl[ied] the statute in [a] special (nongeneric) manner.' Here, we do not reach that question because there is no overlap to begin with. Attempted Hobbs Act robbery does not require proof of any of the elements § 924(c)(3)(A) demands. That ends the inquiry, and nothing in Duenas-Alvarez suggests otherwise."