yes, you are correct. they are called IDC or Insulation Displacement Connectors. these smaller ones in your photo are actually (0.1) in size though ...the larger connectors (0.156) like for the general illumination and whatnot are usually what you hear about needing replacing.
problem with these connecors (the bigger ones, the smaller ones are fine) the connectors are only designed to carry a few amps AT MOST. When these connectors where chosen they failed to notice they were putting upwards of 5 amps through these poor connectors and they get absolutely fried.
The connector part in your photo is also called a "molex Z connector" it allows 2 IDC plugs to be connected together.