Good question.
There are many manufacturers of amps made specially for acoustic guitars with pickups in them. And yes, there is a difference. The biggest difference is that they're designed to distort as little as possible, which means they are usually solid state rather than tube type amps. (Tube amps are usually driven to a point of desired distortion, which is not generally preferred for an acoustic guitar.) There are also a few in the price range you're looking for, and many used ones that you might like. Check eBay for any of the models listed below. One other feature that a lot of acoustic amps have is a microphone input. Since they are not prone to distortion, they work well for vocals. Makes it easy to do a small gig!
Marshall makes their AS50R (Which Scratch uses to very good effect!). It's a fine, very portable 50 watt amp.
There is also a 100 watt version.
Roland has a very good, very compact model (just ask West R Lee).
Check out Laney by chatting with BingK here on this forum.
The Fishman Loudbox series are excellent amps.
Fender makes three:
Acoustisonic SXF - 80 watts,
Acoustisonic Junior, 50 watts, and
Acoustisonic 30 (watts)
SWR makes the large California Blonde and the small Strawberry Blonde.
Peavy makes their Ecoustic 112 and 110 at a nice price point.
Several other popular and very good amps come from Crate, Kustom, Traynor, and others.
Carvin makes the AG100D 100W Acoustic Guitar Amp
Behringer makes several low-cost models , including a tiny 15 watt ULTRACOUSTIC AT108 Acoustic Combo amp that is very inexpensive.
Also, a PA works very well. Maybe a small powered mixer and speaker would serve you.
And, if you ever have nothing BUT money, check out AER. And Genz-Benz makes their Shenendoah model.
There is a lot of room in this topic for analysis paralysis. My advice: Don't study it too long.