Why do police think those two photos are the same person (Thompson murder)?

Not a Bell Gun, a Welrod, a B&T VP9/Station SIX-9, or any other exotic “assassin’s gun”; this is pretty clearly a standard short recoil autoloading pistol with a large suppressor (which can be legally purchased in many states by just paying a federal tax stamp, and can be constructed by a reasonably handy person albeit with questionable reliability) that is experiencing feed or failure to return to battery failures.

Stranger