Why two different heaviside enrichment functions used in XFEM?

I have been looking at XFEM literature for a while and wondering why do we need 2 different heaviside enrichment functions in XFEM? In paper titled "A finite element method for crack growth without remeshing" by Nicolas Moes et al.(1999), they use the following function for heaviside enrichment:

 H(x,y)={1, for y>0

             -1,for y<0}

 While, in paper titled "A review of extended/generalized finite element methods for material modeling" by Ted Belytschko et al.(2009), they use the following function for heaviside enrichment:

 H(x)={0, for x<0

            1,for x>0}

 My question is, when should we use (-1,+1) for heaviside enrichment and when should we use (0,+1) for heaviside enrichment? Or if they mean the same thing? I tried to do a simulation for a semi infinite edge crack problem under impact loading and obtained identical results for stress intensity factors using the 2 different types of heaviside enrichment functions mentioned above! 

Can someone please clarify this to me? I will really appreciate any kind of help/suggestions!

Thanks a lot

abbhuiya