These are unrelated techniques.

Spherical Harmonic Lighting is an alternative or used to supplement the generation of HDR cube maps for the purpose of global illumination. For the very diffuse aspect of this global illumination, Spherical Harmonics are used (Often called light probes), as a very cheap approximation of the environment, that is easy to get in and out of shaders and interpolate between them. They are just a bunch of RGB floats, so you can place a ton of them in the environment to capture a scene's direct or indirect lighting. For specular reflections you still have to use HDR cube maps, as the light probes don't hold enough information for that task.

Blurs are a basic building block of image processing and used in a ton of effects. In a way, there are related topics, as the cube maps generated to cover different roughness factors for PBR rendering are, in-fact blurs! https://threejs.org/docs/#api/en/extras/PMREMGenerator But that's not the topic of the article, but instead of how to do blurs efficiently in real time, in the first place.

You can also use SH to bake directional shadows into meshes, though I'm not sure if I've seen it in a game, just in tech demos