Yes, they are more or less the same console by a different name.

Outside of a few extra features the Famicom provided, such as extra sound channels, the baseline console was more or less the same as the NES, and games had essentially the same visual appearance, with similar but different sound. Also some games allowed you to save your progress whereas the NES port may not have had that feature, such as Metroid.

The two are not different enough to really call them different consoles. Its kinda like a base model car, and one trim level up (but not so high like a sport package, just like an appearance package or leather seats only or something).