"P-996 Lazer", is the name given to describe the fighter jet pictured in the GTA V trailer. In Grand Theft Auto San Andreas, there is a fighter jet similar to this was called a HYDRA, however the "P-996 Lazer" Has no VTOL Capabilities.
In another image (below) released by Rockstar, it shows Micheal flying the Jet. The Jet is armed with Missiles and 2 Cannons which can be seen on the right of the jet, The Missiles have been seen in Grand Theft Auto, San Andreas, but the two cannons on the jet are new.
As far as we know there is only one jet, even though in the second trailer there is one that looks like a harrier and a F-35 While in the Screen shots there is another one that looks like a F-16 and a F-35. This is because The tail is from a F-35 and the front from a SU-27.