Not really. In Japan, the last model released was called Super Famicom Jr., and the last model Famicom was the AV Famicom. In the US (and Europe?), they didn't give them special names. Just NES and SNES, as usual. Fans came up with their own nicknames, like top-loader and mini SNES, but they were never official names.
Now for these "Classic" systems, the offical names are, in Japan:
Nintendo Classic Mini: Family Computer
Nintendo Classic Mini: Super Famicom
in Europe:
Nintendo Classic Mini: Nintendo Entertainment System
Nintendo Classic Mini: Super Nintendo Entertainment System
and in the US:
Nintendo Entertainment System: NES Classic Edition
Super Nintendo Entertainment System: SNES Classic Edition
So in Japan and Europe, they have the word "Mini" in the title, but not in the US.
Also interesting that for NES, the US and Europe systems and games look the same, but Japan is different. But for SNES, Japan and Europe look the same (but have different names), while the US has the "exclusive" look for systems, controllers and cartridges.