So, different alloys or manufacturing treatments was the first possibility that occurred to me. This is the other possibility that occurred to me. That is, two tanks could be physically identical, and one could be rated "LP" and the other "HP" for business decision reasons that have nothing to do with the physical characteristics. I can see how this theory is appealing, since we hear of LP tanks routinely being filled to high pressures in cave country and are said to pass hydro again and again.
There is an actual difference in the steel.
I have some notes somewhere about the details which I can't find right at the moment. But, by memory:
The 3AA specification used for LP cylinders allows any of several alloys to be used, but substantially all cylinders are made using 4130X. However, 4130X is itself a broad classification and many steels with varying properties can be made that fit within the 4130X specification. In any case, 3AA limits the maximum design strength of the steel to 70,000 PSI (at hydro test pressure), and has some requirements on the relationship of tensile to yield strength that are in the specification to limit the brittleness of the steel so that, in the event of a rupture, no fragments are produced.
49 CFR 178.37 - Specification 3AA and 3AAX seamless steel cylinders.
In contrast, the various special permits -- the PST, Worthington and Faber ones are almost identical -- define the composition of the steel much more narrowly. They also define a heat treating and quenching regimen in greater detail. They allow a somewhat higher maximum design strength, and specify a number of tests to limit the brittleness of the steel in place of the limit on the ratio of tensile to yield. These tests include a fold-over test where a cylinder wall must not break when folded over an anvil of relatively small diameter (about 1/4" if I recall correctly), and a test where a cylinder weaked with partial cuts is overpressurized and burst, and must remain in one piece. There is also a test of actual yield strength, and this and some of the other tests must be performed with every lot of cylinders manufacturered. Any of the special permits have these details and are available on the phmsa web site.
The result of all this is that the steel in modern HP cylinder made under the special permits is stronger, so a higher pressure can be used for a given wall thickness, with the same margins of safety.
As an aside, there are some older HP cylinder made under 3AA, that have thicker walls and are much more negatively buoyant. The evolution of design pressures is overall mainly based on the desire to have cylinders be more or less neutral. The higher the design pressure for a given material, the more negative the cylinder will be. This is why, every time the wall composition has changed, we have had a working pressure change, 2640 for most 3AA steels, 3000 for 3AL, and 3442 or 3500 for the special permit steels, and 4000+ for the cabon fiber cylinders.