The difference, of course, is that artificial photosynthesis is a technology which, though it holds great promise, still needs a lot of work at the basic science level before anyone can say for sure that there will be a practical application for it. As Robert Oppenheimer said, scientific breakthroughs don't happen because we want them to happen. They happen because science allows them to happen.
Energy storage technology (or at least much of it) is well past the stage of being a basic science challenge. We know that it works and we know how to deploy it in the field. It is just that experience with grid-connected energy storage is limited and the cost of the technology is high. Energy storage is a technology that cries out for more current deployment, so that experience with it can increase and the cost of storage systems can come down. And, yes, it also cries out for more investment in basic science research on next generation storage technologies, which could further reduce the cost of energy storage systems.