That's a very loosely fitted Interceptor OTV(Outer Tactical Vest) aka IBA. They are made by point blank and are currently being phased out with the IOTV(Army) and MTV(USMC).
There are two levels of protection, the soft armor is inserted into seperate pockets than the hard plates. There are also upgrade kids that add side pockets for side plates and soft armor backings. Soft Armor is generally equated to level IIIA but is not NIJ rated because its front opening and it may or may not stop a .44MAG. The old SAPI rating required it to stop M80 ball, E-SAPI will stop multiple APM2 strikes.
You could wear just the front plate if you wanted to but I question the logic behind that. If you are gonna do that you could get a plate carrier.
These are the enhanced sapi plates, they are slightly curved and have clipped corners.