As Bigedp51 says, they have burning rates in the same sort of area but are not identical - in fact are far apart enough that separate loads data must be consulted and used. Specific energies are fairly close with the H version slightly higher, so they'll produce similar velocities in suitable applications assuming of course that you can get as much of the bulkier IMR version into the case as the ADI / Hodgdon model. (That in theory at any rate makes the IMR version better for cartridges whose cases are a bit too roomy so most powders don't give a 100% case-fill under the bullet, eg 6.5-284 with 140s. Whether it makes a real-life difference is probably questionable.)
As previously said, the H version is slower burning than the I version. I read the reason for this some while back. As bigedp51 says, 4831 for handloading started life as one of B.E. Hodgdon's surplus numbers made by DuPont Industries in WW2 and thrown up surplus after Japan surrendered in 1945. Not only did such powders vary considerably by production lot, but Hodgdon bought and stored so much of this powder, and demand was initially low for what was then regarded as a super-slow (some thought ridiculously slow) burning number in an age when .30-06 was king and there were few people handloading magnums, that the surplus supplies lasted a LONG time. Apparently they became slower burning over these years of storage and by the time the last of it was sold, it was significantly more so than when originally made in 1944/45 or thereabouts.
When 'Bruce' Hodgdon went into business after the war he had two big pluses (apart from his own acumen and immense drive) that saw him succeed against the odds, and did the groundwork for today's successful thriving third generation Hodgdon family powder business - cheap surplus powders and the refusal of the big boys, DuPont, Remington, Winchester etc., to sell components to shooters as they believed that handloading would adversely affect their ammunition sales. By the time that they realised their mistake and belatedly entered the market, the first generation of components entrepreneurs had carved a niche for themselves and for handloading - Hodgdon, Vernon Speer, Joyce Hornady, Fred Huntington (RCBS) - and they'd (especially Bruce H.) put huge amounts of time and effort into popularising handloading writing articles, running workshops giving talks etc. When IMR started selling canister powders for handloaders (early 1960s?) its 4831 was more or less made to the same specification as the WW2 military version, but that was now faster burning than the last of the surplus stuff and warnings had to be issued to stop people who'd worked up absolute max loads in their 270s and similar just substituting the same weight of fresh IMR 4831. When Hodgdon used up its last surplus powder and went to ICI Nobel for continuing supplies it asked the Scottish company to duplicate the slower version, same again when ICI shut down and production went to ADI in Australia.
Having said that, I'm pretty sure all of these powders have changed from the 1950s to today's versions to some extent as they've been developed and improved.