For the children ... there are problems with WHZ and BMI-for-age as these are strongly influenced by body shape and a given threshold may mean different thinks in different populations. I think it is safe to use the term "acute" when there is a rapid loss of weight (could be detected by WHZ, will be detected by MUAC). The term is useful because the conditions referred to are different from chronic conditions such as stunting / stuntedness. These are not either / or conditions. A child can be both stunted and wasted. This is not uncommon. I think a term such as "moderate undernutrition" is confusing as it is unclear what type of undernutrition is being referred to (I would assume it is "WAZ < -2" in the absence of any clues). I prefer to use terms such as "wasting" and "stunting" ot to refer to the indicator used and in (e.g.) "low H/A" or "HAZ < - 2" to avoid confusion. The "terms" acute and "chronic" were once in common usage for adults (as in "Acute Energy Deficiency" and "Chronic Energy Deficiency") but have fallen out of favour. I do not like them because they suggest that undernutrition is all about energy rather than (e.g.) micronutrient deficiencies and pathologies. The matter is also complicated by the absence of growth in adults. This means that acute nutrient deficiencies may take much longer to become apparent in adults than in children. I prefer (as I think you do) the terms "primary" and "secondary". Primary undernutrition develops when nutrient intake is insufficient to provide for normal physiological needs. In adults, primary undernutrition is invariably due to a lack of food in otherwise healthy individuals. Secondary undernutrition occurs when an underlying disease process (for example, HIV/AIDS, TB and cancer) increases metabolic demands and / or decreases food intake or utilisation. The treatment of primary and secondary undernutrition may be quite different. Just my tuppence.