Alternative Representation of the Lipschitz Condition

In some papers, the following condition is often used as an assumption for a function$b: \mathbb{R}^n \to \mathbb{R}^n$:$$\langle b(x)-b(y), x-y\rangle \le K |x-y|^2, \forall x, y \in \mathbb{R}^n.$$

I wonder if this is essentially a form of Lipschitz continuity for the following reason: If $|b(x)-b(y)| \le K |x-y|$ for all $x$ and $y$, then we have$$\langle b(x)-b(y), x-y\rangle \le |b(x) - b(y)| \cdot |x-y| \le K |x-y|^2.$$

Now, I want to understand how much weaker the aforementioned condition compares to Lipschitz continuity. An explicit example satisfying one versus to another is desirable.