Is there really no such thing as a four-leaf clover?

Yes.

What people call a “four-leaf clover” does not technically have four leaves.

Clovers belong to the genus Trifolium, and each clover plant produces a single leaf that is divided into smaller parts called leaflets.

Most clover leaves have three leaflets, which is why the plant’s scientific name means “three leaves.”

A four-leaf clover occurs when that one leaf develops four leaflets instead of the usual three. This happens because of a rare genetic mutation or environmental conditions affecting how the leaf forms.

In botanical terms, the plant still has one leaf made up of multiple leaflets. The familiar lucky symbol is therefore not four separate leaves, but one leaf divided into four parts.

This fact brief is responsive to conversations such as this one.

Sources:
Missouri Botanical Garden: Trifolium repens
Encyclopedia Britannica: Clover
Wikipedia: Leaflet