These are custom covers using custom logos, and as you've said, Nintendo themselves used the term Famicom in the case of the 16-bit follow up and the Japanese 8-bit Gameboy Advance remakes. Famicom may be a made up term, but it's something that Nintendo themselves has recognize. The system lived just long enough to watch its own death. As chip costs dropped, larger games could be fit on cartridges then was possible at introduction of the Family Computer Disk System. The system allowed for role-playing games before current-generation consoles were actually ready for it. When cartridge options became available, the console immediately became obsolete.
Below is the videogame library for browsing at random.
Eggerland
Cleopatra no Mahou
Famicom Grand Prix: F1 Race
Akumajou Dracula
ice Hockey
Falsion
Metroid
Excite Billiards
Bubble Bobble
Section Z
Gyruss
Doki Doki Panic
Othello
Famicom Golf: Japan Course
Mahjong
The Legend of Zelda 2
Pro Wrestling
Nazo no Murasame-Jou
Our Famicom Disk System collection is 15% complete.