All the same rules apply but a pickup w/o trailer would be less likely to be noticed and stopped for inspection.
If the load is visible above the bed and is equipment or machinery obviously not personal property it could attract the attention of a DOT officer and lead to an inspection, particularly if crossing state lines.
Several years ago congress abolished the old Single State Registration system and failed to replace it with an alternative. Without getting into the details this closed a revenue stream to states leaving them seeking other sources of highway revenue. Increased enforcement for fines and greater interest in small commercial haulers resulted so the chance of being noticed and inspected are probably greater now than they once were.
The proper way for a small business to transport small freight quickly is with their own company owned truck with commercial insurance and DOT registration numbers properly displayed, commercial inspection sticker, fire extinguisher, etc. One or more drivers could learn DOT rules, get medical cards, keep a log book, and make the hauls properly. Complying with the law is not difficult. It is actually pretty easy if someone takes the time to learn the rules. Knowing you are legal and have nothing to fear from enforcement officers is comforting.