Two types of stabbing valves that must be prepared for well control are Full Opening Safety Valve (TIW valve) and Inside BOP valve (Gray Valve). We would like to describe what the differences between two valves are.
Full Opening Safety Valve or TIW valve
Full Opening Safety Valve or TIW valve is a ball valve designed for high pressure condition and it can hold pressure from both directions. It is called “Full Opening” because when the ball valve is opened; the flow path through the valve has a smooth inside diameter. One thing that you need to remember is that the term “Full Opening” does not mean that the ID of the valve is the same of drill pipe ID.
Figure 1 Full Opening Safety Valve
The valve should be always located on the rig floor and left in the open position. Additionally, you need to ensure that personnel on the rig have a right wrench to close the valve. The valve left in the open position is critical because the valve can be stab into drill string if the well flows through drill pipe.
For good drilling practices, you must have all size full opening safety valves which can be screwed into each size of drill pipe, drill collar, tubing, etc on the rig. When there is any string in the hole, the correct connection of the valve must be ready on the rig floor to stab in. Furthermore, it is a good practice to install the valve when there is a sting left on the rotary table during rig performs any tasks. The full opening safety valve should be used for shutting the well in while tripping.
Inside BOP valve (Gray Valve)
Insider blowout preventer (IBOP) valves have several industrial names as drill pipe float valves, Gray valves, Omsco valves and drop-in dart valves.
Figure 2 Inside BOP (Dart Type)
This valve is a non-return valve (check valve) allowing pumping through the valve into the drillstring but it prevents upward flow and the more widely used type is “dart-type”. The dart is used to hold the tool open therefore it is possible to stab the valve while the fluid is flowing through the drillpipe. With the IBOP valve installed in the drill string, it allows you to strip in hole without mud flowing through the drillsting. The IBOP valve should not be used for shut the well in while tripping.
Reference book: 
Well Control Books