Speaking only for Texas, upon request for ID by LEO you must produce your CHL license along w/ your DL. As Tate has stated CHL is tied to TX DL and failure to produce CHL after a traffic stop is grounds for revocation of CHL license for 1 year if memory serves. Texas has 2 types of CHL, if one qualifies w/ a semi-auto (SA) one may carry any type of handgun, single, double-action or semi. If one qualifies w/ a double/single action (S) one may only carry a double/single, no semi-auto allowed.
After 5 years and 4-7 stops (no only 2 tickets / speeding) the last time was the only time a LEO asked to take possession of my pistola, I was on scooter and they have terrorist warning about "Banditos" here in space city. He even placed compact 1911 into saddlebag and requested I wait until he reached his shop before I could replace it. While very civil through-out stop I was very suprised as that had never happened before. Most have as your experience bears out been very conversive about what , where, how I liked which ever particular pistol I might have at time.
Mike