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.
Piano is a great instrument. Learning to play at a good level (I'm talking 9 years of practice, exams that test you on music notation, timing, ear etc transfers to other instruments. However it's extremely lonely, and therefore boring, to practicing some bullshit polka that nobody wants to hear. I went to lessons for 9 years, sat 7 grade exams, and quit as soon as I left home. Lessons never taught me to jam, fill in, improvise.
Looking at the Beatles documentary "Get Back", they were just kids with instruments who got to jam full-time. There are plenty of instrumentalists that absolutely kick their asses. What made them special was that they weren't afraid to pay what they wanted to play, and to experiment, together. (They also drove themselves to produce something important to a deadline)
But in this case, to be forced to play only one kind of thing and then not be allowed to try something you want seems really hard. I'm sorry you had to go through that. Thanks for sharing.
Quick story about this comment resonating (pun intended) with me: My son is quietly coming and pulling out my electric guitar from my office room these days and strumming it randomly (just open strings). I haven't said anything except to be careful after he tried to walk it sideways through a door (screams internally in pain). He's watched me practice scales and the wanted to know how to play individual notes so I showed him and left it. A few days later I heard a tiny "ding" of a single note from him for the first time. Still haven't said anything. Maybe he'll love it, maybe he won't.
Basically, I'm going to keep your comment in my mind to not fall into the future trap of denying him something he really wants to try out just because I have some other hope for him. Even now, it'd be easy to jump on my son at this point and say "ho there child, I could send you to some classes now" and then get upset if he doesn't like it. It's really easy to fall for my own bias and whatnot. I'll remind myself to avoid doing that.
If you don't mind me asking, how old were you when you asked for an electric guitar initially?
Later on when I discovered rock and metal music I asked my parents for an electric guitar but they refused, saying I had to play the acoustic I had first and then I could ‘progress’ to electric. I was easily discouraged then so I gave up the idea.
I didnt end up getting an electric guitar and starting to play music seriously until after university when I had a job and could afford it easily myself. Now I play almost every day, learning new things, writing my own little pieces, and jamming with friends. Music is now one of the most fulfilling things in my life, and I believe one of my biggest regrets will be waiting so long to get started after I knew what I wanted!