Some of your California info is inaccurate, but I can see where it came from. In California, all pickups are commercial, even a little Ford Ranger owned by a grandma. If it can't be classified as an RV, it's commercial. You are right about that. However, the real distinction comes from the GVWR. If 11,500 or more, you are not a pickup by definition, and you have to declare max GCW you plan to run, place weight stickers visible, and technically you have to pull into any open scale. And the weight fees are higher than for a "pickup". You can spend close to $1000/year on a new F350 if 11,500 or over. They really don't want you in the scales as they exclude pickups, but by the letter of the law, you must pull in. Fortunately, you can order an F350 SRW with various GVWRs, and the smart choice is to stay under 11,500.
I have a 2021 F250 diesel Tremor, and you are certainly correct that the only difference between it and an F350 is in labeling. Same truck. I tow with it exclusively delivering compact tractors. A typical load is around 10k lbs, and you hardly know a trailer is behind you. I also have a 2019 Raptor and occasionally tow a 5000 lb boat to the river or nearby lake. The Raptor does ok for this light-duty task.
As for a daily driver, 100% I use the Raptor. The F250 is awesome, but unloaded the ride is stiff. It has to be to be such a monster hauling heavy loads. As far as power, both have more than most people can use.