Terminology-wise, local recording is on the device itself is called edge storage (usually with SD cards). You can use edge storage on the network using a decentralized storage system (basically all of the cameras store the footage locally, but you view it from a monitor or handheld device like an iPhone using software that grabs it from each camera), so that's probably why you're not finding what you want - you just need the right search phrases.
What you're looking for (storing cameras to a PC) is called BlueIris: ($30 for one camera or $60 for multiple cameras)
http://blueirissoftware.com/
Most people just use cheap Foscams off Amazon: (there's a million rebranded versions, Foscam just happens to be the most popular)
http://foscam.us/products.html/
The 720p version is only like $65, crazy cheap for being able to pan & tilt & have nightvision. The BlueIris software lets you record to your PC & also stream to your smartphone remote. My buddy has a whole bunch of the cheapo SD cameras setup in his house so he can check on the dogs & the kids from work. The only other kind of setup you could look at is a NAS-based setup (NVR aka Network Video Recorder) from a company like QNAP or Synology, but those get pricey fast.