My Parasol Stars is Taito, but it does not have the logo on the back. All of my other Hucards just has "Hucard" at the bottom corner like in the picture above.
I know it is just cosmetic, but I think the logo adds to the look. Its like the front with the picture, very few Turbo Grafx Hucards had pictures. It seems like most all the PC Engine cards did. I only have one of those that don't, J. League Greatest Eleven.
In the beginning, all of the HuCards published by NEC North America were pretty uniform (no cover art on HuCard). The few third-party titles released early-on (i.e. Tengen, IGS, etc.) had slight variations from this standard.
Later, when NEC North America was transitioning to TTi, we started seeing more package variations (including art on media). Third-parties evolved too: for example, Working Designs used art on HuCards and CD's.
The games with "Taito" on the back, for example, were released later the TG-16's lifespan.
So, in a nutshell, there are at least two factors to consider:
1. At what point in the TG-16 lifespan was the game released? (Things started out homogeneous --> variety)
2. Who published the game in North America? (NEC NA, third-party, TTi)