Welcome to the forum,
These names mean exactly the same thing. The 'acoustic' part of the name means the guitar makes its sound by vibrations of the top (soundboard). So that includes everything that can be played without the need of amplification.
The 'semi' or 'electric' or 'electro' name means that it is wired for sound. In general terms it's a normal acoustic guitar with a pickup of some sort that can plug into an amplifier. This overcomes the problem of playing an acoustic in a large venue and trying to get a microphone in exactly the right place to pick up the sound.
For a beginner there's a simple choice. If you need to make more noise than an ordinary acoustic, or if you need to record your efforts, then a semi is great. If you are happy with the noise level without amplification, and you think you can sit in front of a microphone to record, then you don't need to spend the extra money. (Yes, they are more expensive or there's a trade off in quality)
If our guitars had as many strings as harps, would we change them as often?
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