Clarifying requires a cleansing agent that is both capable of removing product build-up and is at a strong enough concentration that all product build-up will be stripped off. The easiest way to guarantee this is to use a shampoo that is advertised as "clarifying". In these, the cleansing agent is typically sulphates (which will remove 'cones as well as other types of product-based build-up such as oils, waxes, plant extracts, etc.). Regular sulphate-containing shampoos may not have sufficient concentration to remove all build-up (or may contain coating ingredients that will prevent you from attaining a clean slate).
Chelating requires an agent that is both capable of removing mineral build-up and is at a strong enough concentration that it will act to do this. The easiest way to guarantee this is to use a shampoo that is advertised as "chelating" or "swimmer's" (as chelators are the active ingredient in swimmer's shampoos that remove chlorine). In these, the chelating agent is typically EDTA. Many other toiletries also contain EDTA but these are typically in low concentrations where it is used as a pH buffer (to prevent the pH changing if a bit of water or other product gets in the bottle) and so these cannot be used to chelate.
Technique is also important. Unlike with usual washing, the clarifying or chelating shampoo must be massaged thoroughly throughout the entire length of the hair, not just used in the scalp region. As these treatments are stripping and thus can be drying, some people like to use a moisturising treatment after clarifying/chelating.
Personally, I like Pantene's classic clarifying shampoo (the one in a clear bottle with a blue label, NOT the brown bottle / red label one which bizarrely contains 'cones). It is advertised as a clarifyer but IMO it also chelates (well, it certainly removes all the limescale from my sink whenever I use it).
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