The 3D printers you are talking about are very simple. Those are Fused Deposition Modeling and StereoLithography printers.
But there are also 3D printers that work like 2D printers. For example Selective Laser Sintering and PolyJet printers. Just like 2D printers they are very hard to make. Those type of printers are also not available as open source choice.