A small, tight family built on one image: water turning to steam. The base noun אֵד is the vapour itself; from it the verbs describe the act of vaporizing, and by extension vanishing into thin air. This is a final-ה root, so the verbs end in -ות rather than the usual shape. Every word here is verified against pealim, niqqud included.
The same root runs through the verb system. Each binyan is a voice: it bends the one idea into active, passive, causative or reciprocal. Tap to hear.
The contrast is the whole point: pi'el (לְאַדּוֹת) is transitive, you make something evaporate, while hitpa'el (לְהִתְאַדּוֹת) is what the water does to itself: it evaporates, it vanishes. There is no everyday pa'al for this root.
Same root letters, different noun moulds (mishkalim). The mould tells you the function: who does it, the act of doing it, or the thing produced.
Strip the prefixes, suffixes and vowels. Three consonants remain, and the meaning lives there.