I've wondered what Perilla 'Magilla' is also. After growing hundreds of PM plants in various exposures over the past few years in AL (very long season and I usually start spring with cuttings and plants saved over winter, so up to 4-year old material,) and countless Coleus over decades in OH and AL, I believe they are different plants.
I have nothing concrete to offer for evidence, just casual observation of plants in close proximity and sometimes in a same pot. I've never seen PM bloom, which has puzzled me for years. Is there such a thing as a plant that doesn't bloom? I don't think so. What else could it possibly need to do so? One year the plants were in the ground for almost 10 months. A tropical plant should find days any shorter than that quite foreign, so wouldn't it be safe to say it experience any expected variation in light that would occur in a tropical location? It's definitely hot and humid here. Not a nutrient issue, they look great and Coleus inches away make profuse blooms.
I've always questioned calling Coleus by the name Plectranthus. Don't most (all?) other Plectranthus have scented leaves? Aren't the leaves much more meaty/plump? Most Plectranthus I've had would not wilt before I can get inside the house to run a cup of water if I take a cutting.
Once geneticists get to it, the mystery should be solved, and a new name forthcoming, or confirmation of one of many existing names. My money's on confirming Coleus blumeii. No idea what 'they' will say about PM but definitely curious.
But, by any name... they would look as sweet.
Coleus blooming, PM not...
