Well, "commercial" really usually encompasses a whole range of different kinds of contracts depending on the specifics of the load, and there usually are also multiple categories for residential loads, but in the most common case it's simply a matter of the time of day and day of the week that electricity is used.
Commercial use in this general sense is relatively flat throughout the day with little use during night, whereas the residential load profile has peaks in the morning and in the evening with little use late at night and during working hours--it's simply a profile of the average load of a typical household throughout the day vs. the profile of the average load of a "typical business".
Of course, this "typical business" mostly matches offices and retail, industrial users usually have different load profiles, or, for that matter, no real load profile at all, in the sense that they pay based on peak power, not based on energy used, which in effect is an incentive to keep the power profile as flat as possible. Though deviations from that are possible in the form of load shedding, for example, where the utility company can remotely switch off some machinery in the factory to reduce load during peak demand times in exchange for cheaper electricity (this is typically employed with stuff like heating or cooling where it's easy to build your system in such a way that hour long interruptions here and there simply don't matter--your cold storage will stay cool enough even if you stop actively cooling it for an hour, for example).
The overall point is: The utility company doesn't really care what you use the energy for. They don't care whether you produce luxury cars or cheap gadgets. If you are willing to have the lighting in your offices switched off remotely during peak load times, they will happily sell you such a contract for your office building. If you insist on operating your aluminum smelter 24/7, you can have that, though it's going to be expensive. What they care about is the load on their grid and generation facilities, not what you use the energy for.
