The biggest single difference, in practical terms, is that BLO is just RLO that is treated and had some additives put in so that the oil on the outer surface of the wood will "polymerize", which basically means it will harden - not quite dry, but very hard - think of the outer film on old spruce sap.
BLO, once hard, is a little more resistant to water than RLO. If you add a lot of BLO and allow it to "dry" between coats, it can actually build up the surface, fill in grain and sanding lines, etc. Eventually it can start to look like french polish. You sometimes see No.1 rifles that were in service from pre-WW1 up to the 1940's where the surface is smooth like glass and glossy. Some people make the mistake of thinking those rifles have had a modern try-oil application, but that's not always the case. Some of those rifles, particularly the ones at training bases, have just had BLO rubbed in to them a few times a week, over many years, by LOTS of recruits. They are actually beautiful pieces of furniture to behold!
One old trick some aspiring tropes would employ to make the RSM bug the other guy, was to "bone" the surface during oilings. Basically you would take something very like a rib bone (or a real rib bone), and using the linseed oil as a sort of lubricant you would burnish the wood surface with the implement. This would remove many surface imperfections, such as sanding lines, by slightly compressing the outer wood fibres. This is a shortcut to filling in the surface of the wood with many BLO applications. I would not recommend anyone do this on a wartime No.4 rifle.
During WW2, the Commonwealth forces switched to RLO because it was cheaper, more available, and worked basically as well since idle soldiers often spend their time slathering on more oil. If you apply it regularly, both products will keep the wood just as protected.