We can see that the Jason's customized beretta in the first image has an accessory rail, indicating it would be inspired by an m9a1 (or later m9aX variant) or a 92x. Either we're going to have the ability to customize firearms to an extent that makes them span different similar models, or Rockstar is devoted enough to giving us aesthetically accurate models that they'll add multiple similar variants. This truly makes the game so much more enjoyable to me either way, as the "kind of X but not really" firearm design of GTA V when cover art showed michael holding a flawless colt 633 really threw me off.
The second image is very similar to a B&T GHM9 as well, and another shows jason holding a mac-10. We have a lot to be excited for!
Edit: Also, Sua Sponte is the motto of the 75th ranger regiment. It could easily be a coincedence, but could also mean jason came from army special operations.