The biggest difference is in the purpose of each instrument. If you consider both the acoustic guitar and electric guitar as tools for making music, the difference between them comes down the purpose for which you would use each tool. Just as the hammer and the saw are tools with very different purposes, so are the acoustic and electric guitar.
Or, to make the metaphor a little neater, the acoustic guitar vs. the electric guitar is like the bow saw vs. the hacksaw. Both are saws. Both cut things. But you’d use each for a very different purpose.
Practically speaking, I’d say the biggest and most obvious difference, especially for beginners, is that electric guitar requires an amplifier, while an acoustic guitar does not. This means that starting out on acoustic guitar is a little less complicated, not to mention that it saves you a few bucks on your first guitar setup.
However, I think the difference in the purpose of each instrument is the most important idea for beginners to keep in mind when choosing between the two. It’s easy to get hung up on which is easier to play, or to worry about whether you should learn one before the other. However, the real question beginners need to ask themselves is: What do I most want to do as a guitar player?
To succeed, you need to be excited about the music you are learning, or are going to learn someday. If strumming folk or country songs gets you excited about music, you may prefer to learn on an acoustic guitar. If rock music gets you excited, you may be better off with an electric guitar. The tool you would use for folk music is not the same as the tool you’d use for heavy metal.
You choose the right tool for the job.