Wolfe vs Wolfe-Powell stopping conditions

Question

I've been researching line search algorithms recently and there's one detail that is not entirely clear to me. Is there any (practical) difference between Wolfe and Wolfe-Powell stopping conditions?

The mathematical formulation and the constants differ slightly.
The strong Wolfe conditions as described in Nocedal & Wright are basically:

Sufficient decrease (Armijio rule):
$f({\mathbf {x}}_{k}+\alpha _{k}{\mathbf {p}}_{k})\leq f({\mathbf {x}}_{k})+c_{1}\alpha _{k}{\mathbf {p}}_{k}^{{{\mathrm T}}}\nabla f({\mathbf {x}}_{k})$ with $c_{1}=10^{{-4}}$
Curvature
${{\big |}{\mathbf {p}}_{k}^{{{\mathrm T}}}\nabla f({\mathbf {x}}_{k}+\alpha _{k}{\mathbf {p}}_{k}){\big |}\leq c_{2}{\big |}{\mathbf {p}}_{k}^{{{\mathrm T}}}\nabla f({\mathbf {x}}_{k}){\big |}}$ with $c_{2}=0.1$ for non linear CG methods


Now in other texts as this one (§2.3) the strong Wolfe-Powell conditions are defined as:

Sufficient decrease (Armijio rule):
{$f({\mathbf {x}}_{k}+\alpha _{k}{\mathbf {p}}_{k})\leq f({\mathbf {x}}_{k})+\sigma\alpha _{k}{\mathbf {p}}_{k}^{{{\mathrm T}}}\nabla f({\mathbf {x}}_{k})$ with $\sigma\in(0,0.5)$

Curvature
${{\big |}{\mathbf {p}}_{k}^{{{\mathrm T}}}\nabla f({\mathbf {x}}_{k}+\alpha _{k}{\mathbf {p}}_{k}){\big |}\leq -\rho {\mathbf {p}}_{k}^{{{\mathrm T}}}\nabla f({\mathbf {x}}_{k})}$ with $\rho\in [\sigma, 1) $

I've read that the Wolfe-Powell condition should be preferable for conjugate gradients methods that compute the direction ${\mathbf {p}}_{k}$ with the Polak-Ribiere formula.
Is this the actual case? I couldn't find anything on this specific topic. Any insight is much appreciated!