Spring on a name brand second hand electric guitar for your kids you won't regret it. Electric guitars are basically inpossible to damage, and a second hand guitar will retain its value so you'll get those $500-800 bucks back when it turns out your kid wants to do something else. Higher quality guitars have lower action and more comfortable necks which makes them easier to play rewarding your kids more for their efforts.
The fret board isn't the same width.
The notes are in the same places, but that's about it for similarity.
Not when I'm playing Green Day covers on it, it's not.
Also, https://www.youtube.com/watch?v=xMoHRidtQcw
(You're confusing the instrument with the music it's most commonly used to play)
Sure, you can play more or less the same things on both instruments, and anybody who plays electrical will be able to do something on an acoustic guitar and vice versa. But anybody who plays acoustic guitar will also be able to do something on a lute, a mandolin or heck even on a double bass. You will also be able to use your guitar to sound like an organ, a flute, or a synthesizer, with sufficient effect pedals.
For me what makes an instrument is the music it lends itself easily. Give a five year old who never played before an acoustic guitar with fresh strings and an electric guitar plugged into an amp and they will do completely different things with it, because the instruments lend itself to different things. Ironically an electric guitar can be much more direct, because you will hear every slight tiny movement of your fingers amplified. An acoustic guitar (with fresh strings) can be extremely articulate, but you have to put in more energy to produce these sounds.
I certainly see the amplifier as part of the instrument with the electrical guitar, and that alone makes a ton of difference between the two.
Electric and acoustic have a big overlap. Acoustic and classical have a big overlap. Electric and classical have only a tiny overlap.