>It's most likely a solid state drive but still…
It's probably a 120GB or 160GB 2.5" SATA harddrive. I had two netbooks at various times (MSI Wind U100 and an Acer Aspire One) and they both had 160GB of spinning rust, but I know some earlier models of each had 120GB instead. SSDs were still very very expensive at the time netbooks were popular.
But it should be easy to swap out the HD for an SSD on op's machine, the HDs were easy to get to in my netbooks, and it's plain old SATA.
A bigger issue is the battery. These things had only about 2-3 hours of life at best, and replacement batteries for something this old are hard to come by.
Normally I'm the first to advocate repairs over tossing-and-buying-something-new, but a modern x86 chromebook that can run GalliumOS (basically plain old x86 Xubuntu with chromebook-specific configs and drivers set up out-of-the-box) might be a better day-to-day machine than trying to refurbish an Aspire One. I've got an Acer CB-131 that cost me about $150, and has 4GB RAM, 12-13 hours battery life, a 720p IPS display, HDMI out, regular USB ports, the works. There's only 16GB storage, but the SD card reader is designed so that inserted cards fit flush with the body. You can keep a big SD card in there for main storage 24/7 without worrying about it getting broken off.