Let $A$ be a matrix, and $\sigma(A)$ signifies the set of all eigenvalues$(\lambda_i)$ of $A$. Then

An eigenvalue of $A$ that is larger in absolute value than any other eigenvalue is called the dominant eigenvalue.

But

Spectral radius of $A$, which is denoted by $\rho(A)$ is defined as: $\rho(A) = \max\{|\lambda|:\lambda\ \epsilon\hspace{1mm}\sigma(A)$

Thus, spectral radius is more widely applicable; every matrix has a well defined spectral radius. Not every matrix has a dominant eigenvalue but there are theorems guaranteeing the existence of a dominant eigenvalue under appropriate conditions; first among these is the Perron-Frobenius theorem.

Matrices with dominant eigenvalues often arise in numerical approximation schemes for differential equations and the "stiffness" of a system can be quantified in terms of the size of the dominant eigenvalue. Rather than compute the exact value of the dominant eigenvalue, a numerical scheme might use a cheaper estimate of the spectral radius to determine stiffness. This is why both terms are mentioned in your link.