There's a lot of history here. IMR was the norm in the US for many years as developed and manufactured by the Dupont Corporation. Many of the IMR range predate WW2. Post WW2, B.E. (Bruce) Hodgdon bought up large quantities of military surplus IMR powders and sold it repackaged with information on that individual production lots burning rate characteristics. The primary grades were 4895 and 4831, the former used in .30-06 Ball M2 and the latter in 20mm cannon ammunition.
When that source dried up, Hodgdon didn't intend to pack up and find a new trade, rather went around the world looking for new sources - initially ICI Nobel in Scotland and later when it closed down, ADI in New South Wales, Australia. These companies didn't make bespoke tailored versions, rather whatever was closest to IMR-4350 say was renamed H4350 and new loading data published. So, today's H4350 is the third iteration of the product while the original IMR has remained at the same energy and chemical characteristics spec. Throw in another complication in that Hodgdon's original IMR manufactured surplus 4831 lasted a long, long time ..... and slowly changed characteristics during storage becoming slower burning. When the surplus stuff eventually ran out, the customers wanted the 'Hodgdon' version to continue, not revert to faster burning new made IMR spec, so Hodgdon sourced a slower burner from ICI then ADI.
ADI / Thales is one of the most innovative and dynamic manufacturers of smallarms propellants worldwide and has improved its products remarkably in recent years as well as vastly extending the range of grades. The single biggest advance was the 'Extreme' characteristics given to all extruded grades, but every aspect was looked at and imnproived if necessary, a good example being the moved to 'short-cut' grains for better charge densities and more accurate metering in traditional powder measures. The combination of such enhancement, lots of fine gradations in energy content / burning rates across the range, very consistent and high-spec products allied to the 'Extreme' insensitivity to temperature change was much appreciated by the customers, and product / brand loyalty enhanced by Hodgdon's mix of excellent load data, marketing and sponsorship work. IMR meanwhile suffered as Dupont was broken up and production moved elsewhere, but is now finally catching up and under General Dynamics ownership is introducing a new range of 'Enduron' temperature insensitive / copper fouling eraser grades. Although helped by Hodgdon being the information / data producer and marketing / distributing organisation for handloading canister grades, it has long way to go to gain the same degree of customer trust and appreciation.
So far as H4350 and shortages goes, IMR-4350 may or may not be a good stand-in, but the new 'Enduron' IMR-4451 certainly is. It's marginally slower burning, but is an excellent alternative to the H version in cartridges like 260 Rem and 6.5mm Hornady Creedmoor. I'd imagine .30-06 too, although it's a long time since I last loaded this one. (Talking .30-06, it's the old IMR version of 4350 that is the 'classic' powder for this cartridge with 165-180s and the upstart H version is the interloper!)