Light Material is for key lighting in your scene. If you have geometry which you know will be main light source in your scene, such as cove lights and such...
Self illumination is just something that glows, like lava, some glowing features on scifi vehicles or creatures, and so on.
If rendering in unbiased mode, both modes, assuming you have same intensity, will converge to the same result. The thing is that for LightMTL, corona sends special rays to sample for light, while with self illum, corona just samples glowing material as any other material. That means it will be slower if it's small and strong light source. BUT if you sample some complex material with those special samples Corona uses for LightMTL, like material with reflections and refractions, then it can become VERY slow.
So you need to make this decision. It's done this way to prevent people from creating super complex materials that are also emitters, which could result in super slow scenes.
Another use case is camera mapping, or any textures that have baked light information. When you have huge skyscrapers in your scene, and they are textured by textures with baked lighting, you do not want those skyscrapers to be light sources in your scene, for every single polygon of this high poly geometry to be specifically sampled by Corona as a light source, but you still want to not alter that baked lighting by some shading information, and you still want this baked lighting to cast proper global illumination into the scene. That's when you use self illumination.
