Famicom Wars is part of the Advance Wars franchise. The first game in it, in fact.
Famicom, Advance, and Batallion are all really a single franchise.
Whoops, misread, he said Famicom.
The spin-off point stands though.
Oh, and of course, the spin-off point, Fire Emblem, whatever it's simularities with any games in the series, is not a spin-off of any Famicom Wars game, it bears no relation beyond usage of some similar concepts..
And having played quite a few of both franchises, Wars and Fire Emblem, I can say there are quite a few similarities to them. Both have 'fog of war', 'terrain bonuses', a character/unit hierarchy affecting which units can do more damage to which other units (for example, archer and flying mounts in Fire Emblem, anti-aircraft units and choppers in Wars), large and varied maps, a need to constantly supply characters (Wars units need food, gas and ammo. FE characters need weapons, items, and health), there's a concept of 'base capturing' in both, allowing you items in Fire Emblem, and restoration points in Advance Wars)
All of which have been used in other strategy games and/or rpgs and/or tactical rpgs before.
Especially, weapons, items, and health, borrowed from the first rpgs, and the connection with food, gas, and ammo is tenuous at best. Base capturing is just another form of "get/perform the objective", which has been present in every game, ever, from tetris on up, with differing rewards, but always rewards. The whole rock/paper/scissors relationship isn't quite as direct in Advance Wars, and was a concept that existed way before advance wars, since rock/paper scissors. Don't even get me started on strategy games and fog of war.
Then, there are the myrid differences, truthfully they only look similar because they are in very related genres, but compare it to other games in the genres and the connection looks far more tenuous.
There's also the plot advancement through character profiles between and sometimes during battles.
That's sort of been a gaming staple since forever.
Of course as the two series progress they're each establishing themselves with unique touches for individuality, but there's no denying that the same team definitely made both series.
I could say the same for Final Fantasy Tactics, or Ogre Battle.
And while I wouldn't call FE a 'spin-off', FE and Wars are esentially Brother and Sister games.
When compared in a Vacuum, just looking at similarities, everything seems that way. It's called a confirmation bias, people tend to look for positative examples instead of ones that disprove it, like say, the entire leveling-up system, the items system, etc.