I don't have the one for carbon steel handy, but this is from A480 for Stainless, sheet, strip, and plate.

3. Terminology
3.1
Definitions:
3.1.1 Plate, sheet, strip, and cold work as used in this
specification apply to the following:
3.1.2
plate—material 3⁄16 in. [5.00 mm] and over in thick-
ness and over 10 in. [250 mm] in width. Finishes for
plate are actually shown in Section 13.
3.1.3
sheet—material under 3⁄16 in. [5.00 mm] in thickness
and 24 in. [600 mm] and over in width. Finishes for
sheet are actually shown in Section 11.
3.1.4
strip—cold-rolled material under 3⁄16 in. [5.00 mm] in
thickness and under 24 in. [600 mm] in width. Finishes are
detailed in Section 12 for strip , and strip edges in Section 14
for Cold-Rolled Strip.

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Plymouth Tube

kevlar49,

I can't provide the "official definition" you inquired about, but I can provide you a likely explanation of why that requirement exists in your spec.

A rolled rectangular/square bar product would have different grain properties than a similar shape cut from plate. And depending upon which direction the cut "bar" was taken from the plate stock (relative to rolling direction) the mechanical properties could be quite different than a similar shaped rolled product.

As EdStainless noted, with steel there are limits to the product cross section that can be cold finished. With 48" wide plate the practical limit is probably around 3/16" thick. But square bar can be cold finished in sections up to several inches thick. Once again there can be differences in the mechanical properties between hot rolled and cold rolled materials. For example, if your part required a piece of steel say 4"x6"x12" and the BOM simply listed the raw material as type XYZ steel, for limited quantities most vendors would likely purchase the material in the form of sawn plate, since it would be more readily available than bar stock and could be delivered closer to the finished part size, reducing costs for materials and machining.

Hope that helps.
Terry

Some of the description is simply "for convenience" as terms of widths and thicknesses.

But ... Notice the "cold-rolled" term used above? Cold-rolling stock material into shape changes the grain differently from hot-rolled "plate' (so strength and how the material changes during future work (punching, bending, machining, etc) changes. It also changes the finish, the tolerances on that finish, the "shapes" created and sharpness of the corners on those shapes, and the look and feel of the finished item after fabrication.

Internally, we define plate as hot-rolled or hot-rolled + annealed, no cold work. The other point maybe no coiling.
Strip must get involved in cold reduction, and normally it is thinner and narrower, but there is not a strict line.

Quote:

official definition of the difference between bar and plate?

Yes. See below
3.1.1 Plates (other than floor plates) — Flat, hot rolled
steel, ordered to thickness or weight [mass] and
typically width and length, commonly classified as follows....

3.1.4 bars — rounds, squares, and hexagons, of all
sizes; flats 13⁄64 in. (0.203 in.) and over [over 5 mm] in
specified thickness, not over 6 in. [150 mm] in specified
width; and flats 0.230 in. and over [over 6 mm] in specified
thickness, over 6 to 8 in. [150 to 200 mm] inclusive, in
specified width.

Both are definition related to a specific material specification from ASME/ASTM SA/A-6

Just as an aside, in the Stainless world coiled plate has become common.
Often it is 1/2" thick (or more), 60" wide, in 40,000# coils. It sure lets you make large tanks without many welds.
But man is it hard to uncoil...

I have seen specs that allowed you to use cut plate as bar, but there were requirements on the rolling direction.

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Plymouth Tube

Coiled plate is also common for steel plates, 3/16" to 1/4".