A Bug's Life

Hmm, I have helped re-write over 1000 labels for the new labelling regulations & yet I can still be a bit mystified by this. There are technical differences between "extract", "tincture" and a couple of other terms but no-one uses them to my knowledge (which is why I can't remember the other terms). So you tend to just get extracts & flavours.
Malted Barley Extract is an extract derived from malted barley, it could be a flavouring extract but more often the term is used for a colouring extract to give a "natural" brown color instead of the synthetic caramels everyone used to use. Natural Barley Malt Flavouring is similarly a flavour derived from barley malt. There can also be Natural Barley Flavouring, similarly a flavour derived from barley (not malted this time) or Natural Barley Flavouring with other Natural Flavourings. I expect this last is less commonly used as it is a bit of a mouthful & generally thought to be confusing to customers. In fact the technologists that are supposed to write this find it confusing themselves. The last one is a mixture of flavouring derived from barley and other natural flavourings which overall taste of barley.
The "Barley Malt Flavouring" on Brand B is a bit of a contradiction, without the natural epithet the words actually mean a synthetic flavouring which tastes of barley malt, however the bolding of the word barley means it is derived from barley. Most likely it is either Natural Barley Malt Flavouring or Natural BarleyMalt Flavouring with other Natural Flavourings which has been under-declared as a synthetic flavour to make the allergen declaration simpler.
Under the new regulations there is only a requirement to highlight the allergens, not necessarily to explain further but all the supermarkets insist on an explanatory statement along the lines of "for allergens including cereals which contain gluten see ingredients highlighted in bold"
I would suspect that the simplest explanation is that manufacturer of Brand A has been cautious & highlighted the barley even though the gluten content is below the 20mg/kg limit hence you can consume it while Brand B is above that level & sufficient to cause a reaction. For Brand A manufacturer it can be quite challenging to prove that the level is consistently below 20mg/kg.
Hope I've not waffled too much & it makes sense to you & that you are feeling better by now.