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If we stick strictly to what you have writen, then, yes, all commercial vehicles are the same in that they are just that, "commercial vehicles"

Within that very broad & all encompasing heading we will find a wide variety of diferent commercial vehicle types. If we use the term "vehicle" to mean only regristerable, road going machines, we can comfortably leave out Euclid dump trucks & anything else that would not be normally seen on the road. For the purpose of this exchange, i will also leave out any truck above a GVM of whatever you like, but i suspect that we could include vehicles with a payload capacity of up to 2 tons as some of the pickups can easily handle this.

Within the remaining spread we will see utes, pickups, flatbeds, or tray tops. Some of these tray tops are plain, or with fixed sides, or drop sides, or stake sides, some have tiping bodies. Some with special Trade Bodies.
The utes & pickups can be further divided into Utilities & Utility Trucks. The same applies to Pickups & Pickup Trucks, depending on whether they are built on a passenger chassis, [or it's close kin, the "commercial car" chassis], or instead, a true commercial, or even a truck chassis.
We can broaden the descriptive range even further if we want to get into things like fire trucks, some of which have been built onto the lighter chassis, although, these seem to miss the "open back cargo area" boat.

All of these are commercial vehicles.

So to answer the question that you actually asked, then i have to say, Yes, then No, as described above.


Edit. To reply to the last two posts. Lets get one thing clear.
FORD DID NOT INVENT THE UTE. They adopted it

The utility body style was invented by Holden body builders in 1924. Ford copied this style in 1928 [see photo] They then proceded to add a fixed top to this design in 1934, thereby producing a new variant, the "COUPE" utility. To do this, they added their existing "roadster" ute back, to the newly released coupe cabin. The utility body type had been in production for ten years prior to this development.

The name "utility" was applied to this body design by Holden, the original designers & makers of this body design, & this was carried through by the distributors of both Chev & Dodge when these vehicles were offered for sale on the showroom floor. I have seen an original 1924 newspaper ad for the Chev ute, & it was called a Utility in this ad I have also owned the derelict remains of a 1924 Dodge utility. It was clearly a factory made body.

Flatbed, or tray top vehicles had been well known as cargo carriers since the horse & cart days The "tray back" was around long before the ute body type, so while your theory is a good one, it does not reflect the facts.

At the risk of repeating myself, the name "Utility" was applied to a newly designed body style by it's designers & manufacturers in 1924. It refered to a specific design of body, whose decendants are still in manufacture today. The formal Pickup design seems to have appeared at about the same time, or a little earlier, & these used a pressed steel pickup "bed" that was bolted to the chassis, behind the cab, or driving compartment. Same design intent, diferent solution, & we have two diferent vehicles.

The term "buckboard" was often used to describe the tray back bodies that were occasionally fitted to some car chassis in the very early years. This was a direct carry through from the horse drawn vehicle of the same name as they both performed the same basic task, using the same basic design. This term is still to be heard today in some quarters, though not likley in Australia.

All these opinions & theories are just fine, but the word was coined by the originator of the design, & applied by the Distributors of the vehicles that used this body. Nothing has changed.

A Ute is a Ute, & no theory or opinion is going to change that fact.