No way, I just googled trumpet and trombone, and those are different instruments. Electric guitar and classical guitar are just different flavors of the same instrument. Most guitarists play both, if they've ever touched a classical guitar. Playing electric is both easier and less loud, if you don't plug in the amplifier, so they're a lot more suitable for kids than classical guitars. The association that parents have that electric guitars are for adults and acoustic for kids is insane. In my experience good electric guitars are also cheaper than good acoustic, but I have to admit I haven't tried to buy a classical guitar in 20 years.
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.
Electric guitar is all about bending, rhythm, and processed guitar tone. Classical guitar is all about picking tone, speed, and fine variations of touch. (And intonation for the very best players.)
The fret board isn't the same width.
The notes are in the same places, but that's about it for similarity.
As a guitarist who plays both classical and electrical guitar, I must say that I side with the theory that both instruments are more different than they are alike.
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.
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.