CNC is the generic term. A VMC positions the spindle (with the cutting tool) above the table. There are also horizontal mills (HMC), with the table and spindle flopped sideways. Both are "CNC milling machines".
Vertical machine centre (VMC) is a cnc machine with multiple cutting tools which are automatically selected and changed by the machine. and a CNC milling machine has a single tool holder and tool changes are manual.
The basic differace between C.N.C milling and Machining centre is in Milling M/C there is no tool magzine at all.Ie, if a machine is having tool magzine or automatic tool changing mechanisum,then only we can calll as a machining centre.