I was looking for flat LAN cables so it would go under my door to the router located in another room. When I search for "flat ethernet cables" on Amazon, I get a bunch of results on "snagless" ethernet cables.
This is slightly cheaper than flat cables and it's from Belkin.
Do the 2 terms mean the same thing (ie. flat/thin)?
Snag-less is not flat, it has to do with the PVC tabs by the plastic clip that prevent the clip from catching on things when your pulling it past things. I would not get a flat ethernet cable personally, ethernet has electrical EMI and RFI properties that require it to be twisted, and flat cables generally violate those rules.