They are NOT the same. IMR rifle powders (8208 XBR aside) are manufactured by General Dynamics in Canada. Hodgdon extruded grades (plus IMR-8208 XBR) are manufacured by ADI / Thales in Australia. Hodgdon does the marketing, pressure etc testing and distribution for both.
IMR (Improved Military Rifle) was made for many, many years by the huge US DuPont combine and was the primary developer and supplier of propellants to the US military from before WW1 until well after WW2. At the end of WW2, US government sponsored ammunition plants had huge stocks of components for all sorts of calibres in the production pipeline when all orders were abruptly cancelled. Hodgdon got into business by buying these stocks in bulk at very low prices and selling them to the relatively few handloaders around in the early 1950s at bargain prices, also doing a great deal to popularise handloading and educate rifleshooters about what was involved in the process.
Eventually, the surplus powders ran out and Hodgdon had to find suppliers of new manufacture equivalents, it being ICI Nobel in Scotland for extruded numbers and the Olin Corporation (now General Dynamics' St. Marks Powder) plant in St. Marks, Florida for 'spherical' grades. When Nobel shut down, ADI in Australia took on the bulk supply of extruded grades. Meanwhile DuPont divested itself of its explosives, and propellants manufacture was shifted to Canada by the new owners, if nothing else because the US health & safety EPA organisation made it ruinously expensive to produce this type in the USA through new regulations.
Now, the point of all this is that Hodgdon 'copies' of existing IMR powders back in the 1960s or 70s when new production from other sources replaced IMR originals were never exactly the same and there has been not one but two changes of manufacturers in the process. Also, over 50, 60 years the products themselves have evolved with ADI / Hodgdon introducing short-cut versions, the Thales / ADI developed hi-tech coating processes to make its powders temperature tolerant. The fact that both versions have similar (not identical) burning rates is only a single factor out of several - specific energy and density ratings also affect performance as do many other factors.
In one particular example, there was a deliberate specification change - 4831. Both started out the same as Hodgdon acquired and sold bulk IMR-4831 from government stocks (a 20mm cannon propellant) and it proved a very successful product with surplus supplies lasting welll into the 1960s. (Demand for slow burners was a lot lower than today.) Over time, the surplus IMR-4831 dried out a little and this affected the burning rate making is slower. By the time the last of the surplus stock was being sold, it had become significantly slower burning than newly manufactured IMR-4831 from DuPont with a 2gn or so difference in maximum loads in 270 Win for instance. When Hodgdon sourced new supplies it specifically requested that this slower rate be continued as users were used to it and there were safety implications in people not adjusting loads down. This has continued until now.
Of the same name grades, I can't comment on 4198 as I've little experience of this pair, but 4895 generally sees the IMR version allowing slightly heavier charges and sometimes producing higher MVs, the 4350s are close but IMR has longer kernels and space constrained cartridge designs may see IMR need compressed loads where the H version just fills the case, and the 4831s are noticeably different as noted, also having different densities between regular 4831s and the short-cut variety. The members of these pairings can be used as substitutes in almost all cases, but not at identical loadings. Also, there are many examples where a particular cartridge and bullet weight really shines with one or other - H4831sc in L-R .284 Win, 7mm Shehane and 7mm WSM F-Class loadings with 180gn bullets. IMR-4831 can be substituted with reduced max loads, but doesn't do the business nearly as well when you're looking for sub quarter-MOA precision and small velocity spreads. In a 270 Win sporting rifle with 130s with worked up loads for the pair, the user may well not see any difference that matters or finds that the IMR version suits better with say slightly higher MVs. Or, then again, the performance on the hill is not an issue, but the long-grain IMR version is regarded as a pain when it comes to metering in a powder measure with cut grains in the rotor, or the RCBS Chargemaster or similar modern device is more prone to produce over-charges.
