weak inversion region and subthreshold region are the same regions. If you look at the cross section of the layout of a simple mosfet(nmos and pmos) you can see a virtual BJT b/w NMOS and PMOS thru which a current flows: leakage current. When your MOS is off(Vg<Vt) this BJT is still conducting current. When MOS is used as an amplifier (mostly pre amplifiers are biased in subthreshold) in this region we say it is operating in weak inversion region. Then we also have strong inversion and moderate inversion and remember these regions have nothing to do with the cutoff,triode and saturation region of a MOS. Just remember when the MOS is off, you can still bias it with that leakage current and make it act like an amplifier. That region is called weak inversion or subthreshold region.