Car manufacturers are not oil companies. They source their 'own brand' oil from various oil refineries around the world. These can change regularly depending on who offers the best deal at the time and despite apparent advertised endorsement of a particular oil brand. They tend to source from local refineries , so Honda oil sold in Asia will not be exactly the same as Honda oil sold in Europe,or America. (this is also true of well known oil brands) It could be packaged with Hondas own label in 1 litre and 4/5 litre consumer sizes by quite small companies. But they might not bother with large drums, and savvy main dealers might cut out the middle man and buy direct from the actual oil supplier.
Morris and other smaller independent oil blenders buy base oil from a limited number of oil refineries by the tanker load, or 500 litre containers. They blend in additives made by leading chemical companies such as BASF. Quite possibly the same additives used by better known oil brands, who give it some fancy name to impress consumers. Their renowned reputation may all be due to advertising budget ,not because they have developed and made their own additives, or exclusive superior oil base stock that they do not sell to other oil blenders.
Its quite possible that Morris oil would package their oil with the Honda label. I dont know.
But Comma oil (not exactly know as a top brand) say on their website they supplied oil labelled as Comma, Mobil and Toyota. (among others) Comma were at one time owned by mobil so its possible the oil differed for each branding, but would they bother? Easier to use the same stuff, selling it as Comma for the budget market, or at a premium price as Mobil or Toyota. Maybe not quite the same as the likes of Morris and Millers who are smaller independent blenders but they do have their own laboratories, and as long as the oil meets the correct exacting international specification I am happy to accept they have used the correct base oil and additives to achieve it.